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Answer 1 · 2017-05-23T00:22:17

$5.48 \times 10^{5} mL$ $5.48 xx 10^5"mL"$

We'll be using the pressure-volume relationship of gases illustrated by Boyle's law:

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

Solving for $V_{2}$ $V_2$ :

$V_{2} = \frac{P_{1} V_{1}}{P_{2}}$ $V_2 = (P_1V_1)/(P_2)$

We need to have consistent units for the pressure, so let's convert the $575 mm Hg$ $575"mm Hg"$ to atmospheres:

$575cancel("mmHg")((1"atm")/(760cancel("mmHg"))) = 0.757"atm"$

Plugging in known variables, the final volume, in $"mL"$ , is

$V_2 = ((0.757cancel("atm"))(1.00 xx 10^6 "mL"))/(1.38cancel("atm")) = color(red)(5.48 xx 10^5"mL"$