Question #c1c9e

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Question #c1c9e

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Answer 1 · 2014-05-30T22:53:28

The approximate temperature is 20 °C.

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

$P V = n R T$ $PV = nRT$ .

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

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

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

$P V = n R T$ $PV = nRT$

$\frac{P V}{n R}$ $(PV)/(nR)$ = $\frac{n R T}{n R}$ $(nRT)/(nR)$

$\frac{P V}{n R} = T$ $(PV)/(nR) = T$ .

Thus,

$T = \frac{P V}{n R}$ $T = (PV)/(nR)$

Substituting values, we get

$T = (PV)/(nR) = (0.987"atm" × 12"L")/(0.50"mol" × 0.082 06"L·atm·K⁻¹mol⁻¹")$ = 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.

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