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$"Dalton's Law of Partial Pressures"$ states UNEQUIVOCALLY that in a gaseous mixture, the partial pressure exerted by a gaseous component is the SAME as it would exert if it ALONE occupied the container.

And thus $P_"He"=(n_"He"RT)/(V)=((15.2*g)/(4.0*g*mol^-1)xx0.0821*(L*atm)/(K*mol)xx295*K)/(5.00*L)$

$P_"He"=18.4*atm$

$P_(O_2)=(n_(O_2)RT)/(V)=((30.6*g)/(32.0*g*mol^-1)xx0.0821*(L*atm)/(K*mol)xx295*K)/(5.00*L)$

$P_"dioxygen"=4.63*atm$.

$"Dalton's Law of Partial Pressures"$ further states that the total pressure, $P_"Total"$ is the sum of the individual partial pressures.

So here $P_"Total"=P_"He"+P_(O_2)=(18.4+4.63)*atm=23.0*atm$, as required. Have another look at your calcuations. It is all too easy to make an error, and everybody has done this.

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