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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. \((\mathbf{b})\) What assumptions did you make in arriving at your answer?

Short Answer

Expert verified
The estimated molar mass of the unknown gas is approximately \(102.89 \frac{\mathrm{g}}{\mathrm{mol}}\). In deriving this answer, we assumed the volume of the flask remained constant, the gases follow the ideal gas law, and the temperature and pressure remained constant during the filling process.

Step by step solution

01

Identify the Given Information

We're given the following information: 1. The mass increase when the flask is filled with argon gas is 3.224 g. 2. The mass increase when the flask is filled with the unknown gas is 8.102 g. 3. The molar mass of argon is \(39.95 \frac{\mathrm{g}}{\mathrm{mol}}\). We want to estimate the molar mass of the unknown gas.
02

Establish a Relationship

Since we know that the volume of the flask is constant, we can relate the mass increase directly to the number of moles of gas filled in each case. For both argon and the unknown gas, we can write the relationship: \[\frac{\text{mass increase}}{\text{molar mass}} = \text{number of moles}\] For both argon and the unknown gas: \[\frac{\text{mass increase (Argon)}}{\text{molar mass (Argon)}} = \frac{\text{mass increase (Unknown)}}{\text{molar mass (Unknown)}}\]
03

Substitute the Given Values

We will now substitute the values given in the exercise to find the molar mass of the unknown gas. Let \(M_{\text{unknown}}\) denote the molar mass of the unknown gas. \[\frac{3.224 \,\mathrm{g}}{39.95\frac{\mathrm{g}}{\mathrm{mol}}} = \frac{8.102 \,\mathrm{g}}{M_{\text{unknown}}}\]
04

Solve for the Molar Mass

Now, we need to solve for the molar mass of the unknown gas, \(M_{\text{unknown}}\). \[M_{\text{unknown}} = \frac{8.102 \mathrm{~g} \cdot 39.95\frac{\mathrm{g}}{\mathrm{mol}}}{3.224 \,\mathrm{g}} \approx 102.89\frac{\mathrm{g}}{\mathrm{mol}}\]
05

State the Results

The estimated molar mass of the unknown gas is approximately \(102.89 \frac{\mathrm{g}}{\mathrm{mol}}\).
06

Assumptions Made

In arriving at this answer, we made the following assumptions: 1. The volume of the flask is constant for both argon and the unknown gas. 2. The gases follow the ideal gas law, so the relationship between mass, molar mass, and the number of moles holds true. 3. The temperature and pressure during the process of filling the flask with argon and the unknown gas were constant.

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Most popular questions from this chapter

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