Question

what volume (in ml) will a sample of f₂ gas occupy in a syringe at 5.5 atm, if the gas initially has a volume of 25.0 ml at 1.2 atm?
○ 17 ml
○ 3.8 ml
○ 11 ml
○ 5.5 ml

Explanation:

Step1: Identify Gas Law

This problem involves pressure - volume relationship of a gas, so we use Boyle's Law, which states that for a given amount of gas at constant temperature, $P_1V_1 = P_2V_2$. Here, $P_1 = 1.2\ atm$, $V_1=25.0\ mL$, and $P_2 = 5.5\ atm$. We need to find $V_2$.

Step2: Rearrange Boyle's Law

From $P_1V_1=P_2V_2$, we can solve for $V_2$ by rearranging the formula: $V_2=\frac{P_1V_1}{P_2}$.

Step3: Substitute Values

Substitute $P_1 = 1.2\ atm$, $V_1 = 25.0\ mL$, and $P_2=5.5\ atm$ into the formula: $V_2=\frac{1.2\ atm\times25.0\ mL}{5.5\ atm}$.
First, calculate the numerator: $1.2\times25.0 = 30$. Then divide by the denominator: $V_2=\frac{30}{5.5}\approx5.45\ mL\approx5.5\ mL$. Wait, no, wait, let's recalculate: $1.2\times25 = 30$, $30\div5.5\approx5.45$, but wait, maybe I made a mistake. Wait, no, wait, Boyle's Law: when pressure increases, volume decreases. Wait, initial pressure is 1.2 atm, final is 5.5 atm (increase), so volume should decrease from 25 mL. Wait, $V_2=\frac{1.2\times25}{5.5}=\frac{30}{5.5}\approx5.45\approx5.5\ mL$? But let's check again. Wait, $1.2\times25 = 30$, $30\div5.5 = 5.4545\approx5.5\ mL$. But wait, the options are 17 mL, 3.8 mL, 11 mL, 5.5 mL. Wait, maybe I messed up the values? Wait, no, the problem says initial volume is 25.0 mL at 1.2 atm, final pressure 5.5 atm. So $V_2=\frac{1.2\times25}{5.5}=\frac{30}{5.5}\approx5.45\approx5.5\ mL$. So the answer should be 5.5 mL. Wait, but let's check the calculation again. $1.2\times25 = 30$, $30\div5.5 = 5.4545\approx5.5\ mL$. So the correct value of $V_2$ is approximately 5.5 mL.

Answer:

5.5 mL (corresponding to the option "5.5 mL")