77.8k views
11 votes
If 5 mol of oxygen gas effuses through an opening in 10 seconds, how long will it take for the same amount of hydrogen gas to effuse under the same conditions?

( a ) 1.6 s

( b ) 2.5 s

( c ) 40 s

( d ) 160 s

1 Answer

7 votes

Answer:

B

Step-by-step explanation:

Recall the law of effusion:


\displaystyle (r_1)/(r_2) = \sqrt{ \frac{\mathcal{M}_2}{\mathcal{M}_1} }

Because 5 mol of oxygen was effused in 10 seconds, the rate is 0.5 mol/s.

Let the rate of oxygen be r₁ and the rate of hydrogen be r₂.

The molecular weight of oxygen gas is 32.00 g/mol and the molecular weight of hydrogen gas is 2.02 g/mol.

Substitute and solve for r₂:


\displaystyle \begin{aligned} \frac{(0.5\text{ mol/s})}{r_2} & = \sqrt{\frac{(2.02\text{ g/mol})}{(32.00\text{ g/mol})}} \\ \\ r_2 & = \frac{0.5\text{ mol/s}}{\sqrt{\frac{(2.02\text{ g/mol})}{(32.00\text{ g/mol})}}} \\ \\ & = 2.0\text{ mol/s}\end{aligned}

Because there are 5 moles of hydrogen gas:


\displaystyle 5.0\text{ mol} \cdot \frac{1\text{ s}}{2.0\text{ mol}} = 2.5\text{ s}

In conclusion, it will take about 2.5 seconds for the hydrogen gas to effuse.

Check: Because hydrogen gas is lighter than oxygen gas, we expect that hydrogen gas will effuse quicker than oxygen gas.

User Clartaq
by
9.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.