Question #c1c9e

May 30, 2014

The approximate temperature is 20 °C.

To solve this problem, we can use the Ideal Gas Law

$P V = n R T$.

In the formula, $P$ is the pressure, $V$ is the volume, $n$ is the number of moles of gas, $R$ is the Universal Gas Constant, and $T$ is the Kelvin temperature.

We want to solve the Ideal Gas Law for $T$.

To get $T$ by itself, we must divide both sides of the equation by $n R$:

$P V = n R T$

$\frac{P V}{n R}$ = $\frac{n R T}{n R}$

$\frac{P V}{n R} = T$.

Thus,

$T = \frac{P V}{n R}$

Substituting values, we get

$T = \frac{P V}{n R} = \left(0.987 \text{atm" × 12"L")/(0.50"mol" × 0.082 06"L·atm·K⁻¹mol⁻¹}\right)$ = 290 K

Notice how the units cancel to give the temperature in kelvins.

Now we convert to the Celsius temperature:

290 K = (290 - 273.15)°C ≈ 20 °C

Note: I have calculated the answer to only 1 significant figure, because the number of moles and the volume had only 2 significant figures.

The calculated Kelvin temperature had only 2 significant figures. When we subtracted 273.15, we lost one of these significant figures. If you need more precision, you will have to recalculate.