# Question 6f9c1

Aug 1, 2017

See the explanation below to obtain $V = 2.45 \text{L}$.

#### Explanation:

First off, the equation is balanced correctly but rendered incorrectly. A gas is indicated with $\text{(g)}$, not $\text{(s)}$. Thus, properly:

$2 {\text{Na(s)"+"H"_2"SO"_4\rightarrow "H"_2"(g)"+"Na"_2"SO}}_{4}$

With this coreection, proceed to the main calculation.

1. Convert grams to moles of sodium. Render numbers to three significant figures matching those of the given mass, and use the properly rounded atomic mass of sodium from most Periodic Tables:

(5.00"gNa")÷({23.0"g Na"}/{1"mol Na"})=0.217"mol Na"

1. Use the balanced equation to obtain moles of gas:

(0.217"mol Na")×({1"mol H"_2}/{2"mol Na"})=0.108"mol H"_2#

1. Finally convert moles to volume using the Ideal Gas Law. The gas constant $\text{R}$ is rendered as $8.314 \text{J/(mol K)}$ which is commonly quoted in texts, but the volume, like the molar calculation, is expected to be accurate only to three significant figures.

$V = \frac{n R T}{P}$, and T is absolute temperature.

$V = \left(0.108 \text{mol H"_2)×(8.314"J/(mol K"))×(300"K")÷(110,000"Pa}\right)$

$V = 0.00245 \text{m"^3=2.45"L}$, one cubic meter is $1000$ liters.