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Question #e8fd6

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Answer 1 · 2017-04-05T23:00:12

Using Boyle's Law (from the combined Ideal Gas Law), we find that the new volume is 1.409 liters. (See explanation)

Explanation:

We can solve this by using a variation of the Ideal Gas Law (PV = nRT). This variation is the combined Ideal Gas Law:

$\frac{P_{1} V_{1}}{T_{1}} = \frac{P_{2} V_{2}}{T_{2}}$ $(P_1V_1)/T_1=(P_2V_2)/T_2$ , which allows us to compare the changes made to pressure, volume, and temperature.

Since temperature is constant, $T_{1} = T_{2}$ $T_1=T_2$ , so our new comparison would be: (Boyle's Law)

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

We need to find the new volume, $V_{2}$ $V_2$ , so we rearrange the equation:
$V_{2} = \frac{P_{1} V_{1}}{P_{2}}$ $V_2=(P_1V_1)/P_2$

These are the values we have:
$V_{1} = 3$ $V_1=3$ L
$P_{1} = 101$ $P_1=101$ kPa
$P_{2} = 215$ $P_2=215$ kPa

Plug in and solve:
$V_{2} =$ $V_2=$ $\frac{(101 k P a) (3 L)}{215 k P a} = 1.409 L$ $((101 kPa)(3 L))/(215 kPa)=1.409 L$

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