Answer to Question #97088 in General Chemistry for Gabby L Goff

Question #97088
Suppose that 2 mol of gas is measured at 2 atm pressure to have a volume of 5 L, a temperature of 300 K. If the conditions change such that there are 4 mol at 4 atm and at 270 K, what is the new volume?
1
Expert's answer
2019-10-23T07:00:54-0400

Q97088


Solution:

Given:


Initial conditions;

"n_i=2 mol" ---(initial no. of moles)

"P_i=2 atm." ---(initial pressure)

"V_i=5 L" ---(initial volume)

"T_i=300K" ---(initial temperature of gas)


Final conditions;

"n_f=4 mol" ---(final no. of moles)

"P_f=4 atm." ---(final pressure)

"T_f=270K" ---(final temperature)


To find: "V_f" (final volume of the gas)


Using Ideal Gas Law; "PV=nRT"

where, "R=gas constant"


"\\therefore PV\/nT=constant"

"\\implies P_iV_i\/n_iT_i= P_fV_f\/n_fT_f"


"\\therefore V_f=(P_iV_i\/n_iT_i)*(n_fT_f\/P_f)"


Substituting the given values, we get;

"V_f=((2atm*5L)\/(2 mol*300K))" "*(4mol*270K\/4 atm)"

"=4.5L" (Answer)


Thus new volume of the gas is "4.5 L"


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