Question #f9aed

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Question #f9aed

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Answer 1 · 2017-04-17T04:35:14

The final pressure $(P_{2})$ $(P_2)$ is $475 torr$ $"475 torr"$ .

Explanation:

This is an example of Gay-Lussac's law , which states that the pressure of a given amount of a gas is directly proportional to its temperature in Kelvins, if held at constant volume. This means that if the pressure increases, so does the temperature, and vice-versa. The equation to use is:

$\frac{P_{1}}{T_{1}} = \frac{P_{2}}{T_{2}}$ $P_1/T_1=P_2/T_2$

where $P$ $P$ is pressure, and $T$ $T$ is temperature in Kelvins.

The Celsius temperatures must be converted to Kelvins by adding $273.15$ $273.15$ .

Organize the information

Given
$P_{1} = 435 torr$ $P_1="435 torr"$
$T_{1} = 23^{\circ} C + 273.15 = 296 K$ $T_1=23^@"C"+273.15="296 K"$
$T_{2} = 50^{\circ} C + 273.15 = 323 K$ $T_2=50^@"C"+273.15="323 K"$

Unknown: $P_{2}$ $P_2$

Solution
Rearrange the equation to isolate $P_{2}$ $P_2$ . Substitute the given values into the equation and solve.

$P_{2} = \frac{P_{1} T_{2}}{T_{1}}$ $P_2=(P_1T_2)/T_1$

$P_2=(435color(white)(.)"torr"xx323color(red)cancel(color(black)("K")))/(296color(red)cancel(color(black)("K")))="475 torr"$ (rounded to three significant figures)

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Question #f9aed

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