If 200 cm³ of a gas at s.t.p has a mass of 0.268 g, what is its molar mass?

Steps to Solve

1. Identify Given Values

We are given the volume of the gas at standard temperature and pressure (s.t.p) as $200 , \text{cm}^3$ and need to determine its molar mass using its mass.

2. Convert Volume from cm³ to Liters

We need to convert the volume from cubic centimeters to liters because the ideal gas law typically uses liters. Since $1 , \text{L} = 1000 , \text{cm}^3$, we convert:

$$ V = \frac{200 , \text{cm}^3}{1000} = 0.2 , \text{L} $$

3. Use Ideal Gas Law to Find Moles

The ideal gas law is represented as:

$$ PV = nRT $$

Where:

• $P$ is the pressure (1 atm at s.t.p),
• $V$ is the volume in liters (0.2 L),
• $n$ is the number of moles we need to find,
• $R$ is the ideal gas constant ($0.0821 , \text{L} \cdot \text{atm} / \text{K} \cdot \text{mol}$),
• $T$ is the temperature (273.15 K at s.t.p).

Rearranging to find $n$ gives us:

$$ n = \frac{PV}{RT} $$

Now we can substitute the values:

$$ n = \frac{(1 , \text{atm})(0.2 , \text{L})}{(0.0821 , \text{L} \cdot \text{atm} / \text{K} \cdot \text{mol})(273.15 , \text{K})} $$

4. Calculate the Number of Moles

Now, we will calculate the number of moles $n$:

$$ n = \frac{0.2}{0.0821 \times 273.15} \approx 0.0089 , \text{mol} $$

5. Calculate Molar Mass

Now that we have the amount of moles, we can calculate the molar mass ($M$) using the formula:

$$ M = \frac{\text{mass (g)}}{n (\text{mol})} $$

By substituting in the given mass of the gas and the calculated moles:

$$ M = \frac{\text{mass}}{0.0089} $$

6. Final Calculation

Substitute the actual mass (if provided) into the equation to find the molar mass.