Question

a flexible container at an initial volume of 3.10 l contains 9.51 mol of gas. more gas is then added to the container until it reaches a final volume of 14.9 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

Explanation:

Step1: Apply Avogadro's Law

Avogadro's Law is \( \frac{V_1}{n_1}=\frac{V_2}{n_2}\), where \(V_1 = 3.10\space L\), \(n_1=9.51\space mol\), \(V_2 = 14.9\space L\). We need to find \(n_2\).
From \( \frac{V_1}{n_1}=\frac{V_2}{n_2}\), we can solve for \(n_2\) as \(n_2=\frac{V_2n_1}{V_1}\).
Substitute the values: \(n_2=\frac{14.9\times9.51}{3.10}\).
First, calculate \(14.9\times9.51 = 141.699\).
Then, \(n_2=\frac{141.699}{3.10}\approx45.7\space mol\).

Step2: Calculate the moles of gas added

The moles of gas added, \(\Delta n=n_2 - n_1\).
Substitute \(n_2 = 45.7\space mol\) and \(n_1 = 9.51\space mol\).
\(\Delta n=45.7-9.51 = 36.2\space mol\).

Answer:

\(36.2\)