A 3.7 L sample of krypton gas contains 0.638 mol of krypton. How many additional moles of krypton must be added to this sample to expand its volume to 13.3 L? Assume temperature and pressure remain constant. Answer: Next page

To determine how many additional moles of krypton must be added to expand the volume from 3.7 L to 13.3 L while keeping temperature and pressure constant, we can use the ideal gas law relationship, which states that at constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas. Using the formula: \[ \frac{V_1}{n_1} = \frac{V_2}{n_2} \] Where: - \( V_1 \) = initial volume (3.7 L) - \( n_1 \) = initial moles (0.638 mol) - \( V_2 \) = final volume (13.3 L) - \( n_2 \) = final moles (unknown) We can rearrange the equation to solve for \( n_2 \): \[ n_2 = n_1 \cdot \frac{V_2}{V_1} \] Substituting the known values: \[ n_2 = 0.638 \, \text{mol} \cdot \frac{13.3 \, \text{L}}{3.7 \, \text{L}} \] Calculating \( n_2 \): \[ n_2 = 0.638 \, \text{mol} \cdot 3.5946 \approx 2.290 \, \text{mol} \] Now, to find the additional moles of krypton needed, we subtract the initial moles from the final moles: \[ \text{Additional moles} = n_2 - n_1 \] \[ \text{Additional moles} = 2.290 \, \text{mol} - 0.638 \, \text{mol} \approx 1.652 \, \text{mol} \] Therefore, you need to add approximately **1.652 moles** of krypton to expand the volume to 13.3 L.