# 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# ispressurein#"atm"# , if#R = "0.082057 L"cdot"atm/mol"cdot"K"# .#V# isvolumein#"L"# .#n# ismolsof ideal gas.#T# istemperaturein#"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")#