5.A gas of unknown molecular mass was allowed to effuse through a small opening under constant pressure conditions. It required 72.0 seconds for 1.00 L of the gas to effuse. Under identical experimental conditions it required 28.0 seconds for 1.00 L of oxygen gas to effuse. Calculate the molar mass of the unknown gas. Remember that the faster the rate of effusion, the shorter the time required for effusion, the rate is inversely proportional.

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**Effusion of Gases: Calculation of Molar Mass**

**Problem Statement:**

A gas of unknown molecular mass was allowed to effuse through a small opening under constant pressure conditions. It required 72.0 seconds for 1.00 L of the gas to effuse. Under identical experimental conditions, it required 28.0 seconds for 1.00 L of oxygen gas to effuse. Calculate the molar mass of the unknown gas. Remember that the faster the rate of effusion, the shorter the time required for effusion; the rate is inversely proportional.

**Explanation:**

This problem involves applying Graham's law of effusion, which relates to the rates at which two gases effuse. It states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. The equation is:

\[
\frac{{\text{Rate of effusion of gas 1}}}{{\text{Rate of effusion of gas 2}}} = \sqrt{\frac{{\text{Molar mass of gas 2}}}{{\text{Molar mass of gas 1}}}}
\]

In this scenario:
- Gas 1 is the unknown gas.
- Gas 2 is oxygen (O₂), with a known molar mass of 32.00 g/mol.
- Effusion times are given, allowing calculation of effusion rates.

**To Do:**
- Compute the effusion rate (volume per time) for both gases.
- Use Graham's law to find the unknown molar mass.
Transcribed Image Text:**Effusion of Gases: Calculation of Molar Mass** **Problem Statement:** A gas of unknown molecular mass was allowed to effuse through a small opening under constant pressure conditions. It required 72.0 seconds for 1.00 L of the gas to effuse. Under identical experimental conditions, it required 28.0 seconds for 1.00 L of oxygen gas to effuse. Calculate the molar mass of the unknown gas. Remember that the faster the rate of effusion, the shorter the time required for effusion; the rate is inversely proportional. **Explanation:** This problem involves applying Graham's law of effusion, which relates to the rates at which two gases effuse. It states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. The equation is: \[ \frac{{\text{Rate of effusion of gas 1}}}{{\text{Rate of effusion of gas 2}}} = \sqrt{\frac{{\text{Molar mass of gas 2}}}{{\text{Molar mass of gas 1}}}} \] In this scenario: - Gas 1 is the unknown gas. - Gas 2 is oxygen (O₂), with a known molar mass of 32.00 g/mol. - Effusion times are given, allowing calculation of effusion rates. **To Do:** - Compute the effusion rate (volume per time) for both gases. - Use Graham's law to find the unknown molar mass.
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