A container has a volume of #7 L# and holds #12 mol# of gas. If the container is expanded such that its new volume is #14 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?
1 Answer
Jun 30, 2017
#"12 mols ideal gas"# #ul"added"#
This is just an ideal gas law problem:
#PV = nRT#
#P# is pressure in#"atm"# , if#R = "0.082057 L"cdot"atm/mol"cdot"K"# .#V# is volume in#"L"# .#n# is mols of ideal gas.#T# is temperature in#"K"# .
We are told the temperature and pressure must stay constant, and assume a fantastically instantaneous injection of supposedly ideal gas so that the volume doubles. Hence, we can write initial and final states:
#PV_1 = n_1RT#
#PV_2 = n_2RT#
or
#V_1/n_1 = V_2/n_2 = (RT)/P#
Thus, the final mols of gas are:
#n_2 = (V_2/V_1) n_1#
#= ("14 L")/("7 L") xx "12 mols"#
#=# #"24 mols"#
And we should not be fooled --- the question asked for the CHANGE in the mols of gas, i.e.
#color(blue)(Deltan) = n_2 - n_1 = "24 mols - 12 mols"#
#=# #color(blue)("12 mols gas injected")#