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(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))
Commonly known as the Combined Gas Law, the given equation relates the pressure, 
P, volume, 
V, and temperature, 
T, of an ideal gas between its initial (1) and final (2) states. Which of the following shows the final volume in terms of the initial and final pressure, the initial and final temperatures, and the initial volume?
Choose 1 answer:
(A) 
V_(1)=V_(2)
(B) 
V_(2)=(P_(1)T_(2)V_(1))/((T_(1)//P_(2)))
(C) 
V_(2)=(P_(1)T_(2)V_(1))/(P_(2)T_(1))
(D) 
V_(2)=(P_(1)V_(1))/(T_(1))-(T_(2))/(P_(2))
tions | Lesson

P1V1T1=P2V2T2 \frac{P_{1} V_{1}}{T_{1}}=\frac{P_{2} V_{2}}{T_{2}} \newlineCommonly known as the Combined Gas Law, the given equation relates the pressure, P P , volume, V V , and temperature, T T , of an ideal gas between its initial (11) and final (22) states. Which of the following shows the final volume in terms of the initial and final pressure, the initial and final temperatures, and the initial volume?\newlineChoose 11 answer:\newline(A) V1=V2 V_{1}=V_{2} \newline(B) V2=P1T2V1(T1/P2) V_{2}=\frac{P_{1} T_{2} V_{1}}{\left(T_{1} / P_{2}\right)} \newline(C) V2=P1T2V1P2T1 V_{2}=\frac{P_{1} T_{2} V_{1}}{P_{2} T_{1}} \newline(D) V2=P1V1T1T2P2 V_{2}=\frac{P_{1} V_{1}}{T_{1}}-\frac{T_{2}}{P_{2}} \newlinetions | Lesson

Full solution

Q. P1V1T1=P2V2T2 \frac{P_{1} V_{1}}{T_{1}}=\frac{P_{2} V_{2}}{T_{2}} \newlineCommonly known as the Combined Gas Law, the given equation relates the pressure, P P , volume, V V , and temperature, T T , of an ideal gas between its initial (11) and final (22) states. Which of the following shows the final volume in terms of the initial and final pressure, the initial and final temperatures, and the initial volume?\newlineChoose 11 answer:\newline(A) V1=V2 V_{1}=V_{2} \newline(B) V2=P1T2V1(T1/P2) V_{2}=\frac{P_{1} T_{2} V_{1}}{\left(T_{1} / P_{2}\right)} \newline(C) V2=P1T2V1P2T1 V_{2}=\frac{P_{1} T_{2} V_{1}}{P_{2} T_{1}} \newline(D) V2=P1V1T1T2P2 V_{2}=\frac{P_{1} V_{1}}{T_{1}}-\frac{T_{2}}{P_{2}} \newlinetions | Lesson
  1. Multiply by T_2: The Combined Gas Law is given by the equation \left(\frac{P_1V_1}{T_1}\right) = \left(\frac{P_2V_2}{T_2}\right). We need to solve for V_2, the final volume.
  2. Multiply by T11: First, we multiply both sides of the equation by T2T_{2} to get rid of the denominator on the right side of the equation. This gives us (P1V1T1)T2=P2V2(\frac{P_{1}V_{1}}{T_{1}}) \cdot T_{2} = P_{2}V_{2}.
  3. Divide by P22: Next, we multiply both sides of the equation by T1T_{1} to get rid of the denominator on the left side of the equation. This gives us P1V1×T2=P2V2×T1P_{1}V_{1} \times T_{2} = P_{2}V_{2} \times T_{1}.
  4. Divide by T11: Now, we divide both sides of the equation by P2P_{2} to isolate V2V_{2} on one side of the equation. This gives us P1V1T2P2=V2T1\frac{P_{1}V_{1} T_{2}}{P_{2}} = V_{2} T_{1}.
  5. Final Volume Calculation: Finally, we divide both sides of the equation by T1T_{1} to solve for V2V_{2}. This gives us V2=P1V1T2P2T1V_{2} = \frac{P_{1}V_{1} \cdot T_{2}}{P_{2} \cdot T_{1}}.

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