A sample of hydrogen has an initial temperature of 50.° C. When the temperature is lowered to -5.0° C, the volume of hydrogen becomes 212 cm3. What was the initial volume of the hydrogen in dm3?

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A sample of hydrogen has an initial temperature of 50.° C. When the temperature is lowered to -5.0° C, the volume of hydrogen becomes 212 cm3. What was the initial volume of the hydrogen in dm3?

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Answer 1 · 2014-05-30T23:33:49

The initial volume of the gas was 0.255 dm³.

Explanation:

This is an example of Charles' Law.

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$ $V_1/T_1 = V_2/T_2$

$V_{1}$ $V_1$ = ?; $T_{1}$ $T_1$ = (50. + 273.15) K = 323 K

$V_{2}$ $V_2$ = 212 cm³; $T_{2}$ $T_2$ = (-5.0 + 273.15) K = 268.2 K

$V_{1} = V_{2} \times \frac{T_{1}}{T_{2}}$ $V_1 = V_2× T_1/T_2$ = 212 cm³ × $\frac{323 K}{268.2 K}$ $(323"K")/(268.2"K")$ = 255 cm³

$V_{1}$ $V_1$ = 255 cm³ × ${(\frac{1 dm}{10 cm})}^{3}$ $((1"dm")/(10"cm"))^3$ = 0.255 dm³

This makes sense. The initial Kelvin temperature was about 20 % higher than the final temperature. The original volume must also have been about 20 % (40 cm³) larger than the final volume.

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A sample of hydrogen has an initial temperature of 50.° C. When the temperature is lowered to -5.0° C, the volume of hydrogen becomes 212 cm3. What was the initial volume of the hydrogen in dm3?

1 Answer

Explanation:

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