Boyle's Law Problems (Temperature Constant): 1. A gas occupies 5.0 L at 2.0 atm pressure. What will be its volume if the pressure is increased to 4.0 atm, assuming the temperature remains constant?
Answer (1)
[tex]\begin{gathered}\begin{gathered}{\underline{\huge \mathbb{A} {\large \mathrm {NSWER : }}}} \\\end{gathered}\end{gathered}[/tex] To solve the problem using Boyle's Law, we can use the following formula: [tex]P_1V_1 = P_2V_2[/tex] Where: [tex]P_1[/tex] = initial pressure[tex]V_1[/tex] = initial volume [tex]P_2[/tex] = final pressure [tex]V_2[/tex] = final volume Identify the Given Values From the problem statement: [tex]P_1 = 2.0 \text{ atm}[/tex] [tex]V_1 = 5.0 \text{ L}[/tex] [tex]P_2 = 4.0 \text{ atm}[/tex] Rearrange the Formula to Solve for [tex]V_2[/tex] We need to find the final volume [tex]V_2[/tex]. Rearranging the formula gives us: [tex]V_2 = \frac{P_1V_1}{P_2}[/tex] Substitute the Known Values Now, we can substitute the known values into the equation: [tex]V_2 = \frac{(2.0 \text{ atm})(5.0 \text{ L})}{4.0 \text{ atm}}[/tex] Calculate [tex]V_2[/tex] [tex]V_2 = \frac{10.0 \text{ atm} \cdot \text{ L}}{4.0 \text{ atm}} = 2.5 \text{ L}[/tex] Conclusion Thus, if the pressure is increased to 4.0 atm, the volume of the gas will be: [tex]V_2 = 2.5 \text{ L}[/tex] [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/9/2025 [/tex]
