A sample of fluorine ga occupies a volume of 500 ml at 760 torr. Given that the temperature remains the same, calculate the pressure required to reduce its volume by ⅓.
Answer (1)
[tex]\begin{gathered}\begin{gathered}{\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} \\\end{gathered}\end{gathered}[/tex] To calculate the pressure required to reduce the volume of a sample of fluorine gas by one-third while keeping the temperature constant, we can use Boyle's Law. Boyle's Law states that the pressure of a gas is inversely proportional to its volume when the temperature is constant: [tex]P_1V_1 = P_2V_2[/tex] Where: [tex]P_1[/tex] is the initial pressure [tex]V_1[/tex] is the initial volume [tex]P_2[/tex] is the final pressure [tex]V_2[/tex] is the final volume Identify Given Values From the problem, we know: [tex]P_1 = 760 \text{ torr}[/tex][tex]V_1 = 500 \text{ ml}[/tex] The volume is reduced by one-third, so [tex]V_2 = V_1 - \frac{1}{3}V_1 = \frac{2}{3}V_1[/tex] Calculating [tex]V_2[/tex]: [tex]V_2 = \frac{2}{3} \times 500 \text{ ml} = \frac{1000}{3} \text{ ml} \approx 333.33 \text{ ml}[/tex] Use Boyle's Law Now we can apply Boyle's Law: [tex]P_1V_1 = P_2V_2[/tex] Plugging in the known values: [tex]760 \text{ torr} \times 500 \text{ ml} = P_2 \times 333.33 \text{ ml}[/tex] Solve for P₂ To find [tex]P_2[/tex], rearrange the equation: [tex]P_2 = \frac{760 \text{ torr} \times 500 \text{ ml}}{333.33 \text{ ml}}[/tex] Calculating [tex]P_2[/tex]: [tex]P_2 = \frac{380000}{333.33} \approx 1140 \text{ torr}[/tex] Conclusion The pressure required to reduce the volume of the fluorine gas sample by one-third is approximately 1140 torr. [tex]\sf\color{green}{⊱⋅ ────────────────────── ⋅⊰}[/tex][tex]\begin{gathered} \boxed{\begin{array}{cc} \sf \footnotesize \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ···\: ʚ\: \: \: \: \: \: Hope\:it\:helps \: \: \: \: \: ɞ \:··· \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \sf\footnotesize\:\# CarryOnLearning \\ \sf\footnotesize ૮₍´˶ \: • \: . \: • \: ⑅ ₎ა \: \leadsto \footnotesize\sf\color{purple} \underline{Study\:Well!}\end{array}}\end{gathered}[/tex][tex]\sf\color{green}{⊱⋅ ────────────────────── ⋅⊰}[/tex][tex]\large\qquad\qquad\qquad\tt MARCH/13/2025 [/tex]
