A container has a volume of #4 L# and holds #5 mol# of gas. If the container is compressed such that its new volume is #12 L#, how many moles of gas must be released to maintain a constant temperature and pressure?

Question

A container has a volume of #4   L# and holds #5   mol# of gas.  If the container is compressed such that its new volume is #12 L#, how many moles of gas must be released to maintain a constant temperature and pressure?

Nora Arzate · Accepted Answer

15 moles of gas must be released

Applying Avogadro's law here: #v_1/n_1 = v_2/n_2# The initial conditions are denoted by the number 1, and the final conditions are represented by the number 2. • Determine the variables you know and don't know: #color(brown)("Knowns:"# #v_1#= 4 L #v_2#= 12 L #n_1#= 5 mol #color(magenta) ("Unknowns:"# #n_2# • Rewrite the equation to find the total number of moles in the end: #n_2=(v_2xxn_1)/v_1# • Enter the provided values to determine the total number of moles: #n_2=(12cancelLxx5mol)/(4\cancel"L")# = # 15 mol#

Charles Aeschliman · Answer

undefined Using the ideal gas law $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the gas constant, and $T$ is temperature, we can rearrange the equation to solve for the number of moles: $n = \frac{PV}{RT}$. Since temperature and pressure are constant, we can set up a ratio of initial to final volumes: $\frac{V_i}{n_i} = \frac{V_f}{n_f}$. Solving for $n_f$ gives us $n_f = \frac{V_i}{V_f} \times n_i$. Substituting the given values, $V_i = 4 L$, $n_i = 5 mol$, and $V_f = 12 L$, we find $n_f = \frac{4}{12} \times 5 = \frac{5}{3} mol$. Therefore, $n_f = 1.67 mol$. Since the number of moles must be an integer, we round to the nearest whole number. Thus, 2 moles of gas must be released.