Questions: A flexible container at an initial volume of 4.11 L contains 3.51 mol of gas. More gas is then added to the container until it reaches a final volume of 12.1 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container. number of moles of gas: mol

Solution Steps

According to Avogadro's Law, which states that the volume of a gas is directly proportional to the number of moles of the gas when the pressure and temperature are held constant, we can express this relationship as:

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

where:

• \( V_1 \) is the initial volume,
• \( n_1 \) is the initial number of moles,
• \( V_2 \) is the final volume,
• \( n_2 \) is the final number of moles.

Given:

• \( V_1 = 4.11 \, \text{L} \)
• \( n_1 = 3.51 \, \text{mol} \)
• \( V_2 = 12.1 \, \text{L} \)

We need to find \( n_2 \).

Using Avogadro's Law:

\[ \frac{4.11}{3.51} = \frac{12.1}{n_2} \]

Rearrange the equation to solve for \( n_2 \):

\[ n_2 = \frac{12.1 \times 3.51}{4.11} \]

Calculate \( n_2 \):

\[ n_2 = \frac{42.471}{4.11} \approx 10.3333 \, \text{mol} \]

The number of moles of gas added is the difference between the final and initial moles:

\[ \text{Moles added} = n_2 - n_1 = 10.3333 - 3.51 = 6.8233 \, \text{mol} \]

Final Answer