How many atoms are bromine are in 6.41 moles of Br?

Answer:

D. Dependent and Independent Variable

Explanation:

Since the independent variable is already the variable being changed, that is one of the things that can be changed and fromt the independent variable being changed, that changes the dependent variable.

The only things that can change in a valid experiment are dependent and independent variables.

when someone is conducting an experiment, the independent variable is what they change, and the dependent variable is what changes comes because of independent variables, like the independent variable as the cause and the dependent variable as the effect.

so when one is changing the independent variable and dependent varible automatically being changed.

Therefore the correct answer is Dependent and Independent Variable (option D)

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Answer:

ΔE(work)= 692 Kj/mole e⁻ = 4.32 x 10²⁴ eV/mole e⁻

Explanation:

ΔE = hc/λ = (6.63 x 10⁻³⁴j·s)(2.99792 x 10⁸m/s)/(1.73 x 10⁻⁷m) = 1.15 x 10⁻¹⁸j/e⁻ x 6.023 x 10²³ e⁻/mole = 691,999 j/mole e⁻ = 692 Kj/mole e⁻ x 6.24 x 10²¹ eV/KJ = 4.32 x 10²⁴ eV/mole e⁻

Answer:

C. 1.62.

Explanation:

∵ pH = - log[H⁺],

[H⁺] = 0.024 M.

∴ pH = - log(0.024) = 1.62.

So, the right choice is: C. 1.62.

Answer:

Explanation:

1) Chemical equilibrium

2) Equilibrium constant, Kc:

Thus, the equation to use is:

3) Determine the concentration of O₂ (g)

4) Compute Kc

Answer:

B

Explanation:

When work is done, energy is transferred between systems, or transformed from one type of energy into another type. Energy shares the same units of measure as work.

Work and energy are directly related in physics - the amount of work done is the same as the energy transferred. Energy can be defined as the capacity to do work.

Work and energy are directly related concepts in physics. The amount of work done is equivalent to the amount of energy transferred. This is because, by definition, work is done when a force acts on an object to move it some distance, and this process requires energy. Therefore, energy can be viewed as the capacity to do work. If an entity does not contain energy, it cannot perform work. This concept is fundamental to understanding the physics of energy transfer and conservation.

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The overall reaction for the chemical equation in question can be obtained by balancing the equation. The initial equation C2H6 + 7/2O2 → 3H2O + 2CO2 is balanced by multiplying the coefficients by 2 to obtain: 2C2H6 + 7O2 → 6H2O + 4CO2. This represents the overall homogeneous reaction indicating the rate of consumption of reactants and formation of products.

In the realm of Chemistry, the overall reaction for the given chemicals is derived by multiplying each coefficient in the equation by 2, resulting in a balanced equation. Starting with the equation C₂H₆ + 7/2O₂ which leads to 3H₂O + 2CO2, multiplying the coefficients by 2 gives us: 2C₂H₆ + 7O₂ --> 6H₂O + 4CO2. This equation represents the overall reaction observed. It may also depict an elementary reaction showing first-order behavior. The overall reaction equation reflects the stoichiometry of this homogeneous reaction, signaling rates for the consumption of reactants and the formation of products.

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Answer:

48 c

Explanation:

its b on usa test prep

Answer: Option (B) is the correct answer.

Explanation:

According to Le Chatelier's principle, any disturbance causes in an equilibrium reaction will shift the equilibrium in a direction that will oppose the change.

For example, [tex]2NO_{2}(g) \rightleftharpoons N_{2}O_{4}(g)[/tex]

When we increase the temperature then the reaction will shift in a direction where there will be decrease in temperature.

This, means that the reaction will shift in the backward direction.

Thus, we can conclude that if the reaction is at equilibrium and the temperature increases, the equilibrium will shift so that there is more nitrogen dioxide.

Answer:

B. The equilibrium will shift so that there is more nitrogen dioxide.

Explanation:

Hello,

By considering that the mentioned reaction is exothermic, it means that the heat is like a product, if heat is added (increase the temperature) the equilibrium will shift leftwards, contributing to the inverse reaction; it is the formation of more nitrogen dioxide by recalling the Le Chatelier's principle.

Best regards.

Final answer:

The natural abundance of Cl-35 is found by solving for the fraction x in the average atomic mass equation, which corresponds to the percentage. The solution shows that the natural abundance of Cl-35 is 75.77%.

Explanation:

The question is asking us to determine the natural abundance of Cl-35 given the average atomic mass of chlorine and the exact masses of its two stable isotopes, Cl-35 and Cl-37. To find this, we can use the formula for calculating the average atomic mass:

Average atomic mass = (fraction of isotope 1 × mass of isotope 1) + (fraction of isotope 2 × mass of isotope 2)

Let x be the fraction of Cl-35 and (1-x) the fraction of Cl-37. Since the percentages must add up to 100, we have:

35.45 amu = (x × 34.9689 amu) + [(1 - x) × 36.9695 amu]

Rearrange to solve for x:

x = (35.45 - 36.9695) / (34.9689 - 36.9695)

Calculate x and then convert x to a percentage:

x × 100 = percent abundance of Cl-35

Using x = 0.7577 (from given information), we find:

Percent abundance of Cl-35 = 0.7577 × 100 = 75.77%

Therefore, the natural abundance of Cl-35 is 75.77%.

Answer:

E(Z) > E(X)

Explanation:

X => 4.2 x 10¹¹J/50 Nucleons = 8.4 x 10⁹ J/Nu

Z => 8.4 x 10¹¹J/80 Nucleons = 1.1 x 10¹⁰ J/Nu

E(Z)1.1 x 10¹¹J/Nu > E(X)8.4 x 10⁹J/Nu

Answer:

b. 137 g.

Explanation:

Fe₂O₃(s) + 6HCl(aq) → 2FeCl₃(s) + 3H₂O(l),

It is clear that 1.0 mole of Fe₂O₃ react with 6.0 mol of HCl to produce 2.0 moles of FeCl₃ and 3.0 moles of H₂O.

n = mass/molar mass = (100.0 g)/(159.69 g/mol) = 0.6262 mol.

Using cross multiplication:

1.0 mol of Fe₂O₃ react completely with → 6.0 mol of HCl, from stichiometry.

0.6262 mol of Fe₂O₃ produced with → ??? mol of HCl.

∴ The no. of moles of HCl = (6.0 mol)(0.6262 mol)/(1.0 mol) = 3.757 mol.

∴ The mass of HCl needed = no. of moles x molar mass = (3.757 mol)(36.46 g/mol) = 137.0 g.

So, the right choice is: b. 137 g.

To find the required mass of HCl to react with 100 g of rust, calculate the moles of rust, use the stoichiometry of the reaction to find moles of HCl needed, and then convert those moles to grams. The answer is approximately 137 g of HCl.

To determine the mass of hydrochloric acid (HCl) required to react with 100 g of rust (iron (III) oxide, Fe₂O₃), we use stoichiometry based on the balanced chemical equation: Fe₂O₃ (s) + 6HCl (aq) → 2FeCl₃ (aq) + 3H₂O (l).

First, calculate the molar mass of Fe₂O₃ (55.85 g/mol for Fe and 16.00 g/mol for O):

2(55.85) + 3(16.00) = 159.70 g/mol.

Next, calculate the moles of Fe₂O₃ in 100 g:

100 g ÷ 159.70 g/mol = 0.626 moles of Fe₂O₃.

According to the equation, 1 mole of Fe₂O₃ reacts with 6 moles of HCl. Therefore, 0.626 moles of Fe₂O₃3 will react with 0.626 * 6 = 3.756 moles of HCl.

Molar mass of HCl = 36.46 g/mol, so the mass of HCl needed is:

3.756 moles * 36.46 g/mol = 136.93 g, or approximately 137 g.

Thus, option (b) 137 g HCl is the correct answer for the mass of HCl required to react with 100 g of rust.

Answer:

C. That atoms made up the smallest form of matter

Explanation:

The crux of the Dalton's atomic theory is that atoms are the smallest form of matter. He propositioned that atoms is an indivisible particle and beyond an atom, no form of matter exists.

Series of discoveries through time have greatly shaped the Dalton's atomic theory. The discovery of cathode rays by J.J Thomson in 1897 opened up the atom. Atoms were now seen to be made up of some negatively charged particles. Ernest Rutherford through his gold foil experiment proposed the nuclear model of the atom.

Answer:  

[tex]\boxed{\text{0.0301 g}}[/tex]

Step-by-step explanation:  

1. Calculate the initial moles of H₂S

We can use Avogadro's law: the number of moles of a gas is directly proportional to the volume if the pressure and temperature are constant.

[tex]\dfrac{n_{1} }{V_{1}} = \dfrac{n_{2}}{V_{2}}\\\\\dfrac{n_{1}}{\text{44.2 mL}} = \dfrac{1.97 \times 10^{-3} \text{ mol}}{\text{98.5 mL }}\\\\\dfrac{n_{1}}{44.2} = 2.00 \times 10^{-5} \text{ mol}\\\\n_{1} = 44.2 \times 2.00 \times 10^{-5} \text{ mol} = 8.84 \times 10^{-4} \text{ mol}[/tex]

2. Calculate the initial mass of H₂S

[tex]\text{Mass of H$_{2}$S} = 8.84 \times 10^{-4}\text{ mol H$_{2}$S} \times \dfrac{\text{34.08 g H$_{2}$S}}{\text{1 mol H$_{2}$S}} = \text{0.0301 g H$_{2}$S}\\\\\text{The container initially held }\boxed{\textbf{0.0301 g H$_{2}$S}}[/tex]

I think so 4.2, we get the answer when we add together the pressure of each of the gases.

Answer: The total pressure of a mixture is 1.247 atm.

Explanation:

To calculate the total pressure of the mixture of the gases, we use the equation given by Raoult's law, which is:

[tex]p_T=\sum_{i=1}^n(\chi_{i}\times p_i)[/tex]

where,

[tex]p_T[/tex] = total pressure of the mixture

[tex]\chi_{i}[/tex] = mole fraction of i-th species

[tex]p_i[/tex] = partial pressure of i-th species

We are given:

Mole fraction of nitrogen = 0.5

Partial pressure of nitrogen = 1.7 atm

Mole fraction of oxygen = 0.23

Partial pressure of oxygen = 1.1 atm

Mole fraction of argon = 0.12

Partial pressure of argon = 0.7 atm

Mole fraction of methane = 0.10

Partial pressure of methane = 0.5 atm

Mole fraction of water vapor = 0.05

Partial pressure of water vapor = 0.2 atm

Putting values in above equation, we get:

[tex]p_T=[(0.5\times 1.7)+(0.23\times 1.1)+(0.12\times 0.7)+(0.10\times 0.5)+(0.05\times 0.2)][/tex]

[tex]p_T=1.247atm[/tex]

Hence, the total pressure of a mixture is 1.247 atm.

Answer:

D) The nuclei of unstable isotopes  

Explanation:

For example, the carbon-14 in carbon dating is radioactive.

When it decays, a neutron in the nucleus is converted into a proton, an electron, and an antineutrino.

[tex]_{0}^{1}\text{n} \longrightarrow \, _{1}^{1}\text{p} + \, _{-1}^{0}\text{e} + \overline{\nu}_{\text{e}}[/tex]

The water would need to B. absorb less energy during the plateau in order to melt.  

Salt when added to ice lowers the freezing point of the ice. So, if ice is added to the solid ice it doesn't let it to freeze rather the temperature of water may fall but it won't freeze.

For melting, it needs less energy after adding salt because salt itself absorbs the energy from the surroundings to help the phase transition of water from solid to liquid.

Answer: C. It would need to absorb more energy during the plateau in order to melt.

Explanation:

adding salt lowers the freezing point, meaning it needs to absorb more energy from its surrounding in order to melt.

Answer:

ΔH(mix'g)= 42.3Kj/mole

Explanation:

ΔH = (mcΔT)water/moles X

m = mass(g) = 20ml x 1.00g/ml = 20 g

c = 4.184 j/g⁰C

ΔT = 25°C- 15°C = 10°C

moles X = (1.5g)/(76g/mole) = 0.0197 mole X

ΔH = (20g)(4.184j/g°C)(10°C)/(0.0197 mole X) = 42,300J/mole = 42.3Kj/mole (3 sig.figs.)  

The enthalpy change for the reaction per mole of substance X, which dissolves in water and increases the temperature from 15.0 °C to 25.0 °C, is calculated to be 41.8 kJ/mol. The positive sign indicates the reaction is exothermic.

The first step is to calculate the amount of heat (q) released during the reaction. We use the formula q = mcΔT, where m is the mass of the water (density x volume = 1 g/mL x 20.0 mL = 20.0 g), c is the specific heat capacity of water (4.18 J/g⋅∘C ), and ΔT is the change in temperature (25.0 ∘C - 15.0 ∘C = 10.0 ∘C). Therefore, q = 20.0 g x 4.18 J/g⋅∘C x 10.0 ∘C = 836 J.

Next, we calculate the number of moles of X using the formula n = mass / molar mass = 1.50 g / 76.0 g/mol = 0.02 mol.

Finally, we calculate the enthalpy change (ΔH) per mole of X using the formula ΔH = q/n, therefore ΔH = 836 J / 0.02 mol = 41800 J/mol. Since the standard unit for enthalpy change is kJ/mol, we convert it from J/mol to kJ/mol by dividing by 1000 to get ΔH = 41.8 kJ/mol.

Notice that the answer is positive indicating that heat energy is released to the surroundings, which means the reaction is exothermic.

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Each of the four quantum numbers for an electron in an atom represents a specific characteristic and has specific rules regarding which values are allowed. The principal quantum number n can be any positive integer, the azimuthal quantum number l ranges from 0 to n - 1, the magnetic quantum number ml ranges from -l to +l, and the spin quantum number ms can either be +1/2 or -1/2. The quantum numbers 2, 1, 0, 1; 3, 1, 0, -1/2; 4, 2, -1, -1/2 from the provided list are valid.

To evaluate the possible set of quantum numbers, it is important to understand the rules that govern the values for each quantum number. The quantum numbers are expressed in the form (n, ℓ, mℓ, ms). Each one of these represents a certain feature of a given electron in an atom.

The first quantum number n, known as the principal quantum number, denotes the electron's energy level and can be any positive integer starting from 1.

The second quantum number ℓ, known as the azimuthal or angular momentum quantum number, is responsible for the shape of the electron's orbital and can have values ranging from 0 to n - 1.

The third quantum number, mℓ, known as the magnetic quantum number, describes the orientation of the electron's orbital. It can have values between -ℓ and +ℓ including 0.

Lastly, the fourth quantum number ms, the electron spin quantum number, can have one of two values: +1/2 or -1/2, denoting the two possible spin states of an electron.

Using these rules, we can verify the following quantum numbers: 4, 2, 3, -1/2, 2, 1, 0, 1, 3, 1, 0, -1/2, 4, 3, -2, 1/2, -3, 2, 2, -1/2, 4, 2, -1, -1/2, 2, 2, 2, 1/2, 3, 2, -3, 1/2. It is evident the following quantum numbers are valid: 2, 1, 0, 1; 3, 1, 0, -1/2; 4, 2, -1, -1/2.

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Answer:

P = 3.8 Atm = 2900 mmHg  (2 sig.figs.)

Explanation:

PV = nRT => P = nRT/V = (1.9 moles)(0.08206LAtm/molK)(228K)/9.45L  = 3.76 ~ 3.8 Atm x 760mmHg/Atm =2888 mmHg ~ 2900 mmHg (2 sig.figs.)

2900 mmHg is the pressure of 1.9 mols of nitrogen gas in a 9.45 L tank and at a temperature of 228 K.

"Pressure" is defined as the thrust (force) applied to a surface per area. The force to area ratio is another way to describe it (over which the force is acting). The height of a mercury column that precisely balanced the mass of the columns of atmosphere above the barometer is used to measure atmospheric pressure, which is also referred to as barometric pressure.

It can be stated using a number of various measurement methods, including millimeters (or inches) of mercury, pounds every square inch (psi), dynes per square centimeter (dyn/sq cm), millibars (mb), standard atmospheres, as well as kilopascals.

PV = nRT

P = nRT/V

(1.9 moles)(0.08206LAtm/molK)(228K)/9.45L  = 3.76

3.8 Atm x 760mmHg/Atm =2888 mmHg

=2900 mmHg

Therefore, the pressure is 2900 mmHg.

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Answer: K

Hope this helps you out!

Answer:

Potassium (K)

Explanation:

The reason that potassium is the more reactive metal is because it is in group 1, as opposed to group 11 for copper, and being in group 1 means that it has one valence electron, which it can give away by reacting with almost any other element, and in doing so, it becomes much more stable.

Answer:

1:2:1:2

Explanation:

A molecule is made up of aggregates of small particles called atoms.

                   CH₄ + 2O₂ → CO₂ + 2H₂O

From the reaction above we have: 1 molecule of methane CH₄ reacting with 2 molecules of oxygen gas O₂ to produce 1 molecule of carbon dioxide gas CO₂ and 2 molecules of H₂O:

                   CH₄ + 2O₂ → CO₂ + 2H₂O

                      1    :     2   :     1      :     2    

Answer:

True

Explanation:

Answer:

True

Explanation:

The half lives of unstable isotopes of elements vary from miliseconds to billions of years, for example Bismuth-209 has the longest half life known by the human and the scientists and it has still billions of years to this day, and there are elements that cannot withstand seconds before decaying into another element, so the statement is True.

Answer:

Explanation:

The specific question is how many moles of Ba(OH)₂ are present in 285 mL of 0.800 M Ba(OH)₂.

In a titration, the determination of the number of moles of the substance whose molarity is known, is the first step of the calculations.

Since you know the molar concentration, and the volume of the substance, in this case the base Ba(OH)₂, you can use the molarity formula to solve for the number of moles:

The name of the variables are:

Formula:

Solve for n:

Substitute the known values>

Answer: 0.288 moles of Ba(OH)₂.

Note that from the number of moles of one component (the base, in this case), you can calculate the molar concentration of the other component (the acid in this case),  because, at the equivalence point, both acid and base reactants are at the theoretical mole ratio, i.e. both are consumed.

Final answer:

To calculate the number of moles of Ba(OH)2 present in 285 mL of 0.800 M Ba(OH)2, multiply the volume (0.285 L) by the molarity (0.800 M), resulting in 0.228 moles of Ba(OH)2.

Explanation:

To determine the number of moles of Ba(OH)2 present in 285 mL of 0.800 M Ba(OH)2, we first convert the volume in milliliters to liters by dividing by 1000:

285 mL ÷ 1000 = 0.285 L

Now, by using the concentration of the Ba(OH)2 solution (Molarity, M), we can calculate the moles of Ba(OH)2:

Number of moles = Molarity (M) × Volume (L)

Number of moles = 0.800 M × 0.285 L

Number of moles = 0.228 moles

Therefore, there are 0.228 moles of Ba(OH)2 in the 285 mL of the solution provided by the chemist during the titration.

Answer:

[tex]\boxed{\text{0.20 g}}[/tex]

Explanation:

We know we will need a balanced chemical equation with molar masses, volumes, and concentrations, so, let's gather all the information in one place.

M_r:                       84.01

                 HCl + NaHCO₃ ⟶ NaCl + H₂O + CO₂

V/mL:        200.

c/mol·L⁻¹:  0.012

(a) Moles of HCl

[tex]\text{Moles of HCl} =\text{0.200 L HCl} \times \dfrac{\text{0.012 mol HCl}}{\text{1 L HCl}}\\\\=\text{0.0024 mol HCl}[/tex]

(b) Moles of NaHCO₃

The molar ratio is 1 mol NaHCO₃ = 1 mol HCl

[tex]\text{Moles of NaHCO$_{3}$}= \text{0.0024 mol HCl} \times \dfrac{\text{1 mol {NaHCO$_{3}$}}}{ \text{1 mol HCl}}\\\\= \text{0.0024 mol NaHCO$_{3}$}[/tex]

(c) Mass of NaHCO₃

[tex]\text{Mass of NaHCO$_{3}$}= \text{0.0024 mol NaHCO$_{3}$} \times \dfrac{\text{84.01 g {NaHCO$_{3}$}}}{ \text{1 mol NaHCO$_{3}$}}\\\\= \textbf{0.20 g NaHCO$_{3}$}\\\\\text{The man would need to ingest }\boxed{\textbf{0.20 g}} \text{ of NaHCO$_{3}$}.[/tex]

Answer:

D.Cardboard pieces

Explanation:

Cardboard pieces would a good representation of the crust.

The crust of just a thin layer in terms of thickness. We can picture the crust as an apple skin or an orange peel. It's thickness is averages about 5-10km for thinner oceanic crusts and about 30-50km for thicker continental crust.

The crust is the thinnest layer of the earth.

Below the crust is the region of the mantle. The mantle is made of the upper mantle, asthenosphere and mesosphere. The asthenosphere is in a weak plastic form and it is very thick. It averages a thickness of about 190km,about 100 times the oceanic crust and 4 times the continental crust. The mantle is the thickest region of the earth.

The core is the innermosr layer of the earth. It is about 2300km thick.

It would be very ideal to relatively represent the crust as pieces of cardboard floating on an oily asthenosphere.

Answer:

12,742 km

Explanation:

Therefore, its radius is 6,371 km.

Answer:

12,742 km

Explanation:

radius is 6,371 km.

Answer:

For a substance to classify as a mineral, it must lie within certain parameters. It should be an inorganic solid, that is naturally occurring in nature (not synthesized), with an ordered internal structure and a definite chemical composition.

By definite chemical composition, geologists mean that the mineral must be have chemical constituents that have an unvarying chemical composition, or a chemical composition that oscillates withing a very limited and specific range.

An example is the mineral, halite. It has a chemical composition of one sodium atom and one chloride atom, represented as NaCl and is unchanging in this composition throughout nature.

To determine the number of molecules of sodium oxide created, we can use the given balanced chemical equation, molar mass, and Avogadro's number. The reaction equation tells us that for every 4 moles of sodium, 2 moles of sodium oxide are formed. From the given mass of oxygen, we can calculate the number of moles of sodium oxide and then convert that to molecules using Avogadro's number.

To determine the number of molecules of sodium oxide created, we need to use the given balanced chemical equation and the molar mass of sodium oxide (Na2O). From the balanced equation, we can see that 4 moles of sodium (Na) react with 1 mole of oxygen (O2) to form 2 moles of sodium oxide (Na2O). Thus, the stoichiometry of the reaction tells us that for every 4 moles of sodium, 2 moles of sodium oxide are formed.

Using the molar mass of sodium oxide, which is 61.98 grams/mol, we can calculate the number of moles of sodium oxide formed from the given mass of oxygen. First, convert the mass of oxygen to moles by dividing it by the molar mass of oxygen, which is 32.0 grams/mol. So, 187 grams of oxygen is equal to 5.84 moles. Based on the stoichiometry of the reaction, for every 1 mole of oxygen, 2 moles of sodium oxide are formed. Therefore, 5.84 moles of oxygen will form 11.68 moles of sodium oxide.

Finally, to determine the number of molecules of sodium oxide, we can use Avogadro's number, which states that 1 mole of any substance contains 6.02 x 10^23 particles (atoms or molecules). So, multiplying the number of moles of sodium oxide by Avogadro's number, we get:

11.68 moles x 6.02 x 10^23 molecules/mol = 7.03 x 10^24 molecules of Na2O

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Answer:

At least four such rinses.

Explanation:

Let [tex]c_n[/tex] denotes the concentration of the residue after the [tex]n[/tex]th rinse. [tex]n[/tex] can be any non-negative integer (which includes zero.)

The initial concentration of the solution in the flask is [tex]\rm 0.900\;M[/tex]. That is:

[tex]c_0 = \rm 0.900\;M[/tex].

[tex]\rm 1.00\;mL[/tex] of this [tex]\rm 0.900\;M[/tex] solution is left in the flask after it is emptied for the first time.

The [tex]\rm 9.00\;mL[/tex] solvent will increase the volume of the solution from [tex]\rm 1.00\;mL[/tex] to [tex]\rm 10.00\;mL[/tex]. At this point the number of moles of solute in the flask stays unchanged. The concentration of the residue will drop to [tex]1/10[/tex] of the initial value. That is:

[tex]\displaystyle c_1 = \rm \frac{1}{10}\;c_0 = \frac{1}{10}\times 0.900\;M[/tex].

Repeat this process, and the concentration of the residue will drop by a factor of [tex]1/10[/tex] again. That is:

[tex]\displaystyle c_2 = \rm \frac{1}{10}\;c_1 = \frac{1}{10}\times (\frac{1}{10}\times 0.900\;M) = {\left(\frac{1}{10}\right)}^{2}\times 0.900\;M[/tex].

Summarize these values in a table:

[tex]\begin{array}{l|cccc}\text{Number of Rinses} & 0 & 1 & 2 & \dots \\[0.5em]\displaystyle\text{Concentration}\atop\displaystyle\text{of the residue}& \rm 0.900\;M & \rm\dfrac{1}{10}\times 0.900\;M &\rm {\left(\dfrac{1}{10}\right)}^{2}\times 0.900\;M \dots \end{array}[/tex].

The trend in [tex]c_{n}[/tex] is similar to that of a geometric series with

Again, refer to the trend in [tex]c_{n}[/tex] as the value of [tex]n[/tex] increases. The general formula for [tex]c_{n}[/tex], the concentration after the [tex]n[/tex]th rinse, will be:

[tex]\displaystyle c_{n} = \rm {\left(\frac{1}{10}\right)}^{n}\; 0.900\;M[/tex].

As a side note, [tex]0 < 1/10 < 1[/tex]. As a result, the value of [tex]c_{n}[/tex] will decrease but stay positive as the value of [tex]n[/tex] increases. Increasing the number of rinses will indeed reduce the concentration of the residue.

In other words, what's the minimum value of [tex]n[/tex] for which [tex]\c_{n} \le \rm 0.000100\;M[/tex]?

Recall that

[tex]\displaystyle c_{n} = \rm {\left(\frac{1}{10}\right)}^{n}\; 0.900\;M[/tex].

As a result, [tex]n[/tex] should satisfy the condition:

[tex]\displaystyle \rm {\left(\frac{1}{10}\right)}^{n}\; 0.900\;M \le 0.000100\;M[/tex].

Multiply both sides by

[tex]\displaystyle \frac{1}{\rm 0.900\;M}[/tex],

which is positive and will not change the direction of the inequality:

[tex]\displaystyle \rm {\left(\frac{1}{10}\right)}^{n} \le \frac{0.000100}{0.900}[/tex].

Take the natural logarithm [tex]\ln[/tex] of both sides of the inequality. The function [tex]\ln(x)}[/tex] is increasing as [tex]x[/tex] increases on the range [tex]x > 0[/tex]. This function will not change the direction of the inequality, either.

[tex]\displaystyle \rm \ln\left[{\left(\frac{1}{10}\right)}^{n}\right] \le \ln\left(\frac{0.000100}{0.900}\right)[/tex].

Apply the power rule of logarithms: [tex]n[/tex] is an exponent inside the logarithm. That will be equivalent to an expression where [tex]n[/tex] is a coefficient in front of the logarithm operator:

[tex]\displaystyle \rm \ln\left[{\left(\frac{1}{10}\right)}^{n}\right]  = n\cdot \left[\ln{\left(\frac{1}{10}\right)}\right][/tex].

[tex]\displaystyle n\cdot \left[\ln{\left(\frac{1}{10}\right)}\right]\le \ln\left(\frac{0.000100}{0.900}\right)[/tex].

Multiply both sides by

[tex]\displaystyle \frac{1}{\ln \left(\dfrac{1}{10}\right)}}[/tex].

Keep in mind that logarithms of numbers between 0 and 1 (excluding 0 and 1) are negative. The reciprocal of a negative number is still negative. The direction of the inequality will change. That is:

[tex]\displaystyle n\cdot \left[\ln{\left(\frac{1}{10}\right)}\right]\times \frac{1}{\ln \left(\dfrac{1}{10}\right)}}\ge \ln\left(\frac{0.000100}{0.900}\right)\times \frac{1}{\ln \left(\dfrac{1}{10}\right)}}[/tex].

The right-hand side is approximately 3.95. However, [tex]n[/tex] has to be an integer. The smallest integer that is greater than 3.95 is 4. In other words, it takes at least four such rinses to reduce the residual concentration to under 0.000100 M (0.000090 M to be precise.) Three such rinses will give only 0.00900 M.

Final answer:

Through serial dilution principles, the minimum number of rinses needed to dilute the residual concentration of a solution in a flask to 0.000100M or below is approximately 7, considering a 1:10 dilution ratio for each rinse.

Explanation:

The question involves calculating the minimum number of rinse cycles required to reduce the residual concentration of a solution adhering to the walls of a flask below a target concentration, using serial dilution principles.

After each rinse, the concentration is diluted by the volume ratio, in this case, a 1:10 dilution per rinse because 1.00 ml of the original solution is mixed with 9.00 ml of solvent. The formula for the final concentration (Cf) after n rinses is given by Cf = Co × (Vo / Vt)n, where Co is the original concentration, Vo is the original volume adhering to the flask, Vt is the total volume after adding solvent, and n is the number of rinses.

To solve for n, we rearrange the equation to get n = log(Cf/Co) / log(Vo/Vt). Plugging in the given values (Co=0.900M, Cf=0.000100M, Vo=1ml, Vt=10ml), we find that the minimum number of rinses needed to reduce the concentration to 0.000100 M or below is calculated to be around 7. The exact number might slightly vary depending on rounding during calculation, but 7 rinses ensure meeting the target concentration threshold.

Answer:

[tex]\boxed{\text{positive deviation}}[/tex]

Explanation:

[tex]\text{If the molecules interact less favourably in the solution than in the individual}\\\text{liquids, they can break away more easily than they can in the separate liquids.}\\\text{There will be more molecules in the vapour phase than you would expect.}\\\text{The solution will show a } \boxed{\textbf{positive deviation}} \text{ from Raoult's Law.}[/tex]