A sample of gas occupies 17 mL at -112°C. What volume does the sample occupy at 70°C?

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A sample of gas occupies 17 mL at -112°C. What volume does the sample occupy at 70°C?

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Answer 1 · 2016-02-07T16:05:42

Use Charles' Law, which states that at a constant pressure, temperature and volume are proportional.

It is also written as

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$ $("V"_1)/("T"_1)=("V"_2)/("T"_2)$

Before we define our values, note that temperature in gas law equations always use Kelvin, not Celsius.

To go from degrees Celsius to Kelvin, add $273$ $273$ .

Thus, we have

$V_{1} = 17 mL$ $"V"_1="17 mL"$
$T_{1} = - 112^{\circ} C = 161 K$ $"T"_1=-112^@"C"="161 K"$

$V_{2} = ? ? ?$ $"V"_2=???$
$T_{2} = 70^{\circ} C = 343 K$ $"T"_2=70^@"C"="343 K"$

Thus, we have

$\frac{17 mL}{161 K} = \frac{V_{2}}{343 K}$ $("17 mL")/("161 K")="V"_2/("343 K")$

Cross-multiply to solve for $V_{2}$ $"V"_2$ :

$17 \cdot 343 mL \cdot K = 161 K \cdot V_{2}$ $17 * "343 mL" * "K"="161 K" * "V"_2$

$5831 mL = {161 V}_{2}$ $"5831 mL"="161 V"_2$

$V_{2} = 36.2173913043 mL$ $color(red)("V"_2="36.2173913043 mL"$

The question technically has $1$ $1$ significant figure, since there's only one significant figure in $70^{\circ} C$ $70^@"C"$ .

This means the final answer is

$V_{2} = 4 \times 10^{1}$ $color(blue)("V"_2=4xx10^1$ $mL$ $color(blue)("mL"$

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A sample of gas occupies 17 mL at -112°C. What volume does the sample occupy at 70°C?

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