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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