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Chapter 10: Problem 107

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 approximately 100.98 g/mol. We assumed that the same volume and pressure were used for both argon and the unknown gas, the unknown gas behaves as an ideal gas, and the temperature remains constant throughout the experiment.

Step by step solution

01

Gather the given information

We are given the following information: - Mass increase when flask is filled with argon gas: 3.224 g - Mass increase when flask is filled with unknown gas: 8.102 g - Molar mass of argon: 39.95 g/mol Assume that the same volume and pressure of gas were used in both cases. As we don't have those values, we'll use V and P as placeholders in the calculations.
02

Calculate the moles of argon gas

First, we'll calculate the moles of argon gas using the mass increase value and the molar mass of argon. The formula for calculating moles (n) is: n = mass / molar_mass Plugging in the given values, we get the moles of argon gas: n(Ar) = 3.224 g / 39.95 g/mol ≈ 0.0807 mol
03

Apply the ideal gas law to determine volume and pressure

The ideal gas law is given by: PV = nRT where: - P is the pressure - V is the volume - n is the number of moles - R is the ideal gas constant (8.314 J/mol·K) - T is the temperature in kelvins. We are not given the temperature, but since the conditions are the same for both argon and the unknown gas, we can assume that the temperature is constant. Converting the ideal gas law into a relationship between moles (n) and volume and pressure (V and P), we get: V and P = n R T For argon, we have: V and P(Ar) = 0.0807 mol * R * T
04

Calculate the moles of unknown gas

Since, according to ideal gas law, PV = nRT, and we're assuming the pressure and temperature are the same for both argon and the unknown gas, we can infer that: m(Ar)*M(unknown) = m(unknown)*M(Ar) Where m is mass and M is molar mass. Rearranging, we find the molar mass of the unknown gas: M(unknown) = (m(unknown) * M(Ar)) / m(Ar) Plugging in the given values: M(unknown) = (8.102 g * 39.95 g/mol) / 3.224 g ≈ 100.98 g/mol
05

State assumptions and final answer

The molar mass of the unknown gas is approximately 100.98 g/mol. The assumptions we made in the process of solving the problem are: 1. The same volume and pressure were used for both argon and the unknown gas. 2. The unknown gas also behaves as an ideal gas. 3. The temperature remains constant throughout the experiment.

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