What volume will a 300.0 mL sample of a gas at STP occupy when the pressure is doubled at constant temperature?

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What volume will a 300.0 mL sample of a gas at STP occupy when the pressure is doubled at constant temperature?

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Answer 1 · 2015-11-25T10:52:04

$150.0 mL$ $"150.0 mL"$

Explanation:

When number of moles and temperature are kept constant, pressure and volume have an inverse relationship - this is known as Boyle's Law.

In simple terms, when pressure increases, volume decreases, and when pressure decreases, volume Increases.

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Mathematically, this is written as

$P_{1} V_{1} = P_{2} V_{2}$ $color(blue)(P_1V_1 = P_2V_2)" "$ , where

$P_{1}$ $P_1$ , $V_{1}$ $V_1$ - the pressure and volume at an initial state
$P_{2}$ $P_2$ , $V_{2}$ $V_2$ - the pressure and volume at a final state

So, if pressure doubles, what would you expect to happen to the sample's volume?

Well, the only way the product between the pressure and the volume would remain constant is if the volume would be halved.

Now, you don't need to know the actual values of the two pressures, all you need to know is the relationship that exists between them.

$P_{2} = 2 \cdot P_{1}$ $P_2 = 2 * P_1$

This means that you have

$P_{1} V_{1} = P_{2} V_{2} \Rightarrow V_{2} = \frac{P_{1}}{P_{2}} \cdot V_{1}$ $P_1V_1 = P_2V_2 implies V_2 = P_1/P_2 * V_1$

$V_2 = color(red)(cancel(color(black)(P_1)))/(2 * color(red)(cancel(color(black)(P_1)))) * V_1 = 1/2 * V_1$

$V_2 = 1/2 * "300.0 mL" = color(green)("150.0 mL")$

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What volume will a 300.0 mL sample of a gas at STP occupy when the pressure is doubled at constant temperature?

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