Answered

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Gab wants to have a portable oxygen tank. a 5.00 liter oxygen gas exerts a pressure of 1.00 atmosphere. how much pressure is needed for this gas to be compressed in a 2.00 liter cylinder, provided there is no temperature change?

Sagot :

SOLUTION:

Step 1: List the given values.

[tex]\begin{aligned} & P_1 = \text{1.00 atm} \\ & V_1 = \text{5.00 L} \\ & V_2 = \text{2.00 L} \end{aligned}[/tex]

Step 2: Calculate the final pressure by using Boyle's law.

[tex]\begin{aligned} P_1V_1 & = P_2V_2 \\ P_2V_2 & = P_1V_1 \\ \frac{P_2V_2}{V_2} & = \frac{P_1V_1}{V_2} \\ P_2 & = \frac{P_1V_1}{V_2} \\ & = \frac{(\text{1.00 atm})(\text{5.00 L})}{\text{2.00 L}} \\ & = \boxed{\text{2.50 atm}} \end{aligned}[/tex]

Hence, the pressure needed for the gas to be compressed in a 2.00 liter cylinder is 2.50 atm, provided that there is no temperature change.

[tex]\\[/tex]

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