Answer :
Use the Equation of Clapeyron:
[tex]\frac{P_1.V_1}{T_1}=\frac{P_2.V_2}{T_2}\\ \\ \frac{0.5V_1}{235}=\frac{1.2*48}{320}\\ \\ 320*0.5V_1=235*1.2*48\\ \\ V_1=\frac{235*1.2*48}{320*0.5}=84.5 liters[/tex]
[tex]\frac{P_1.V_1}{T_1}=\frac{P_2.V_2}{T_2}\\ \\ \frac{0.5V_1}{235}=\frac{1.2*48}{320}\\ \\ 320*0.5V_1=235*1.2*48\\ \\ V_1=\frac{235*1.2*48}{320*0.5}=84.5 liters[/tex]
The initial volume of the gas is 117L.
What is volume?
Volume is the amount of space the matter occupies.
What do you mean by combined gas law?
- The combined gas law combines the three gas laws: Boyle's Law, Charles' Law, and Gay-Lussac's Law.
- It states that the ratio of the product of pressure and volume and the absolute temperature of a gas is equal to a constant.
- When Avogadro's law is added to the combined gas law, the ideal gas law results.
- It is a combination of the other gas laws that works when everything except temperature, pressure, and volume are kept constant.
- There are a couple of common equations for writing the combined gas law. The classic law relates Boyle's law and Charles' law to state:
PV/T = k
where P = pressure, V = volume, T = absolute temperature in K and k= constant.
- Another common formula for the combined gas law relates before and after conditions of a gas:
P1V1 / T1 = P2V2 / T2
Where P1 and P2 = initial and final pressure in atm
T1 and T2 = Initial and final temperature in K
V1 and V2 = initial and final volume in L
Using combined gas law:
P1V1/T1 = P2V2/T2
Given:
P1 = 0.5 atm
T1 = 325K
P2 = 1.2 atm
V2 = 48L
T2 = 320K
Assuming that the number of moles are constant for both conditions:
(P1 x V1)/T1 = (P2 x V2)/T2
Substituting the given values,
(0.5 x V1)/325 = (1.2 x 48)/320K
Solving for V1
V1 = (1.2atm x 48L x 325K)/ (320Kx 0.5 atm)
V1 = 117L
Hence, the initial volume of the gas is 117L.
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