Questions: 4. 0.820 mole of hydrogen gas has a volume of 2.00 L at a certain temperature and pressure. What is the volume of 0.125 mol of this gas at the same temperature and pressure? A. 0.0512 L D. 4.01 L B. 0.250 L E. 19.5 L C. 0.305 L

Solution Steps

According to Avogadro's Law, at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of the gas. This can be expressed as:

\[ \frac{V_1}{n_1} = \frac{V_2}{n_2} \]

where \( V_1 \) and \( n_1 \) are the initial volume and moles, and \( V_2 \) and \( n_2 \) are the final volume and moles.

From the problem, we know:

• \( n_1 = 0.820 \) moles
• \( V_1 = 2.00 \) L
• \( n_2 = 0.125 \) moles

We need to find \( V_2 \).

Using the relationship from Avogadro's Law:

\[ \frac{2.00 \, \text{L}}{0.820 \, \text{mol}} = \frac{V_2}{0.125 \, \text{mol}} \]

Solving for \( V_2 \):

\[ V_2 = \frac{2.00 \, \text{L} \times 0.125 \, \text{mol}}{0.820 \, \text{mol}} \]

\[ V_2 = \frac{0.2500 \, \text{L}}{0.820} \]

\[ V_2 \approx 0.3049 \, \text{L} \]

Final Answer