A 1.09-g sample of an unknown gas has a volume of 505 mL and a pressure of 711 mm Hg at 56.2 °C. Calculate the molar mass of this compound.

To calculate the molar mass of the unknown gas, we can use the **Ideal Gas Law** equation:

\[
PV = nRT
\]

Where:
- \(P\) is the pressure,
- \(V\) is the volume,
- \(n\) is the number of moles,
- \(R\) is the ideal gas constant, and
- \(T\) is the temperature in Kelvin.

### Step 1: Convert units to appropriate SI units.
1. **Pressure (P)**: Convert from mm Hg to atm (atmospheres).
\[
P = 711 \, \text{mm Hg} \times \left(\frac{1 \, \text{atm}}{760 \, \text{mm Hg}}\right) = 0.9355 \, \text{atm}
\]

2. **Volume (V)**: Convert from mL to L.
\[
V = 505 \, \text{mL} \times \left(\frac{1 \, \text{L}}{1000 \, \text{mL}}\right) = 0.505 \, \text{L}
\]

3. **Temperature (T)**: Convert from Celsius to Kelvin.
\[
T = 56.2^\circ C + 273.15 = 329.35 \, \text{K}
\]

4. **R (Ideal Gas Constant)**: Use \(R = 0.0821 \, \text{L·atm/mol·K}\).

### Step 2: Solve for the number of moles (\(n\)) using the Ideal Gas Law.
Rearrange the Ideal Gas Law to solve for \(n\):
\[
n = \frac{PV}{RT}
\]

Substitute the known values:
\[
n = \frac{(0.9355 \, \text{atm})(0.505 \, \text{L})}{(0.0821 \, \text{L·atm/mol·K})(329.35 \, \text{K})}
\]

\[
n = \frac{0.4725}{27.0421} = 0.01747 \, \text{mol}
\]

### Step 3: Calculate the molar mass.
Molar mass (\(M\)) is calculated as the mass (\(m\)) divided by the number of moles (\(n\)):

\[
M = \frac{m}{n}
\]

Substitute the known values:
\[
M = \frac{1.09 \, \text{g}}{0.01747 \, \text{mol}} = 62.37 \, \text{g/mol}
\]

### Final Answer:
The molar mass of the unknown gas is **62.37 g/mol**.

---

Would you like further details on any of the steps? Here are some related questions:

1. How does the Ideal Gas Law relate to real gases at high pressures or low temperatures?
2. What is the difference between an ideal and a real gas?
3. How does the molar mass of a gas influence its properties?
4. What are common examples of gases with similar molar masses?
5. How can this calculation be applied in a laboratory setting?

**Tip:** Always ensure units are consistent when applying gas laws to avoid calculation errors.

Learn how to calculate the molar mass of a 1.09-g sample of an unknown gas at 711 mm Hg and 56.2 °C. This problem demonstrates the use of the Ideal Gas Law, unit conversions, and molar mass formula. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation