Question
What will be the pressure of the gaseous mixture when $$0.5\,L$$ of $${H_2}$$ at $$0.8\,bar$$ and $$2.0\,L$$ of $${O_2}$$ at $$0.7\,bar$$ are introduced in a $$1\,L$$ vessel at $$27{\,^ \circ }C?$$
A.
$$1.8\,bar$$
B.
$$2.8\,bar$$
C.
$$3.0\,bar$$
D.
$$5\,bar$$
Answer :
$$1.8\,bar$$
Solution :
$$\eqalign{
& {\text{Partial pressure of hydrogen gas :}} \cr
& {V_1} = 0.5\,L\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{V_2} = 1.0\,L \cr
& {P_1} = 0.8\,bar\,\,\,\,\,\,\,\,\,\,{P_2} = ? \cr} $$
$${\text{Applying Boyle's law}}$$ $${\text{(At constant }}T{\text{ and }}n{\text{)}}$$
$$\eqalign{
& {P_1}{V_1} = {P_2}{V_2}\,\,\,{\text{or}}\,\,\,{P_2} = \frac{{{P_1}{V_1}}}{{{V_2}}} \cr
& \therefore \,\,{P_2} = \frac{{\left( {0.8\,bar} \right) \times \left( {0.5\,L} \right)}}{{\left( {1.0\,L} \right)}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 0.40\,bar \cr
& {\text{Partial pressure of oxygen gas :}} \cr
& {V_1} = 2.0\,L,\,\,\,\,\,\,\,\,\,\,\,{V_2} = 1.0\,L \cr
& {P_1} = 0.7\,bar\,\,\,\,\,\,\,\,{P_2} = ? \cr
& {\text{or}}\,\,\,{P_2} = \frac{{{P_1}{V_1}}}{{{V_2}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{\left( {0.7\,bar} \right) \times \left( {2.0\,L} \right)}}{{\left( {1.0\,L} \right)}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1.40\,bar \cr
& {\text{Pressure of the gas mixture,}} \cr
& {P_{mix}} = {P_{{H_2}}} + {P_{{O_2}}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = 0.40 + 1.40 \cr
& \,\,\,\,\,\,\,\,\,\,\,\, = 1.80\,bar \cr} $$