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Chapter 10: Problem 104

When a large evacuated flask is filled with argon gas, its mass increases by 3.224 \(\mathrm{g}\) . When the same flask is again evacuated and then filled with a gas of unknown molar mass, the mass increase is 8.102 g. (a) Based on the molar mass of argon, estimate the molar mass of the unknown gas. (b) What assumptions did you make in arriving at your answer?

Short Answer

Expert verified
The molar mass of the unknown gas is estimated to be 100.4 g/mol. We made the following assumptions: the volume, temperature, and pressure of the flask remain the same for both gases; the unknown gas behaves as an ideal gas; and Avogadro's hypothesis holds true for both gases.

Step by step solution

01

Identify the given information and the variables

We are given the mass increase for the argon gas and the unknown gas. We can denote the mass increase of the argon gas as m₁=3.224 g and the mass increase of the unknown gas as m₂=8.102 g. We also know the molar mass of argon gas M₁=39.95 g/mol. We need to calculate the molar mass of the unknown gas, which we can denote as M₂.
02

Calculate number of moles of argon gas

We can calculate the number of moles of argon gas using the mass of argon gas and its molar mass. The formula to find the number of moles (n) is: n = mass / molar mass For argon gas, we can write: n₁ = m₁ / M₁ n₁ = 3.224 g/ 39.95 g/mol n₁ = 0.0807 mol
03

Apply Avogadro's hypothesis

Avogadro's hypothesis states that equal volumes of gases at the same temperature and pressure have the same number of moles. As we are assuming that the volume, temperature, and pressure of the flask remain the same for both gases, we can apply Avogadro's hypothesis. Since the number of moles is the same for both gases, we can write: n₁ = n₂ 0.0807 mol = n₂
04

Calculate the molar mass of the unknown gas

Now that we know the number of moles of the unknown gas, we can find its molar mass using the mass of the unknown gas. We can use the formula: M₂ = m₂ / n₂ M₂= 8.102 g / 0.0807 mol M₂ = 100.4 g/mol The estimated molar mass of the unknown gas is 100.4 g/mol.
05

Identify assumptions made in the calculations

The following assumptions were made during the calculations: 1. The volume, temperature, and pressure of the flask remain the same for both gases. 2. The unknown gas behaves as an ideal gas. 3. Avogadro's hypothesis holds true for both gases. Finally, the molar mass of the unknown gas is estimated to be 100.4 g/mol.

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Most popular questions from this chapter

(a) Calculate the number of molecules in a deep breath of air whose volume is 2.25 L at body temperature, \(37^{\circ} \mathrm{C},\) and a pressure of 735 torr. (b) The adult blue whale has a lung capacity of \(5.0 \times 10^{3} \mathrm{L}\) . Calculate the mass of air (assume an average molar mass of 28.98 \(\mathrm{g} / \mathrm{mol}\) ) contained in an adult blue whale's lungs at \(0.0^{\circ} \mathrm{C}\) and \(1.00 \mathrm{atm},\) assuming the air behaves ideally.

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Indicate which of the following statements regarding the kinetic-molecular theory of gases are correct. (a) The average kinetic energy of a collection of gas molecules at a given temperature is proportional to \(m^{1 / 2}\) . (b) The gas molecules are assumed to exert no forces on each other. (c) All the molecules of a gas at a given temperature have the same kinetic energy. (d) The volume of the gas molecules is negligible in comparison to the total volume in which the gas is contained. (e) All gas molecules move with the same speed if they are at the same temperature.

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At constant pressure, the mean free path \((\lambda)\) of a gas molecule is directly proportional to temperature. At constant temperature, \(\lambda\) is inversely proportional to pressure. If you compare two different gas molecules at the same temperature and pressure, \(\lambda\) is inversely proportional to the square of the diameter of the gas molecules. Put these facts together to create a formula for the mean free path of a gas molecule with a proportionality constant (call it \(R_{\text { mfp }}\) , like the ideal-gas constant) and define units for \(R_{\operatorname{mfp}}\) .
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