Answer: 1.624 L
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Boyle's Law states volume of a gas at a constant temperature varies inversely with the pressure, or
[tex]P_1V_1 = P_2V_2[/tex]
From the problem you're told that, intially, [tex]P_1 = 406\:kPa[/tex] and [tex]V_1 = 4 \: L[/tex]. Then, you're told that the pressure increases to [tex]P_2 = 1000 \: kPa[/tex]. Plug these values in and solve for the new volume, [tex]V_2[/tex]:
[tex]P_1V_1 = P_2V_2\\
(406\:kPa)(4 \: L) = (1000 \: kPa)V_2\\
V_2 = 1.624 \: L[/tex]
