A gas occupies 50 L at a pressure of 2 atm. What is the volume when the pressure is increased to 10 atm?

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A gas occupies 50 L at a pressure of 2 atm. What is the volume when the pressure is increased to 10 atm?

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Answer 1 · 2017-05-31T02:27:39

$10$ $10$ $L$ $"L"$

Explanation:

We're asked to calculate the new volume of a gas when its pressure is increased.

To solve this, we can use the pressure-volume relationship of gases, illustrated by Boyle's law:

$P_{1} V_{1} = P_{2} V_{2}$ $P_1V_1 = P_2V_2$

where

$P$ $P$ is the initial ( $1$ $"1"$ ) and final ( $2$ $"2"$ ) pressure of the gas, and
$V$ $V$ is the initial ( $1$ $"1"$ ) and final ( $2$ $"2"$ ) volume of the gas.

Let's plug in our known variables, and rearrange this equation to solve for the final volume, $V_{2}$ $V_2$ :

$V_2 = (P_1V_1)/(P_2) = ((2cancel("atm"))(50"L"))/(10cancel("atm")) = color(red)(10"L"$

Thus, when the pressure of the gas was increased by a factor of $5$ ( $2"atm"$ to $10"atm"$ ), the volume decreased by a factor of $5$ ( $50"L"$ to $10"L"$ ).

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A gas occupies 50 L at a pressure of 2 atm. What is the volume when the pressure is increased to 10 atm?

1 Answer

Explanation:

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