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A gas is initially at a pressure of 0.43 atm, and a volume of 11.7 liters. Then the pressure is raised to 3.61 atm and the volume is decreased to 9.5 liters. This causes the temperature to raise to 627 K. What was the initial temperature of the gas? A. 83.19 K B. 7.32 K C. 327.97 D. 91.98 K

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Answer:

D. 91.98K

Explanation:

The General Gas Law equation is given by,

[tex] \frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}[/tex]

From the question,

the initial pressure,

[tex]P_1 = 0.43 \: atm[/tex]

the initial volume,

[tex]V_1 = 11.7 \: litres[/tex]

the final temperature,

[tex]T_2=627K[/tex]

the final pressure,

[tex]P_2=3.61atm[/tex]

the final volume,

[tex]V_2=9.5litres[/tex]

Making

[tex]T_1[/tex]

the subject of the expression, we obtain

[tex]T_1= \frac{P_1V_1T_2}{P_2V_2} [/tex]

By substitution,

[tex]T_1= \frac{0.43 \times11.7 \times627}{3.61 \times9.5} [/tex]

[tex]T_1=91.980K[/tex]

Hence the initial temperature was 91.98 K

The Initial temperature was 92.24 K

Further Explanation;

Boyle's law

  • Boyle's law states that the volume of a fixed mass of a gas is inversely proportional to its pressure at a constant temperature.
  • That is;

[tex]P\alpha \frac{1}{V}[/tex]

[tex]P = \frac{k}{V}[/tex], where k is a constant

Charles' Law

  • Charles's law states that the volume of a fixed mass of a gas is directly proportional to absolute temperature at constant pressure.
  • That is; [tex]V \alpha T\\ V= kT[/tex], where k is a constant

Combined gas law

  • Combined gas law combines both Boyle's law and Charles's law.
  • It states that the volume of a fixed mass of a gas is directly proportional to absolute temperature and inversely proportional to pressure.

That is;

[tex]\frac{P_{1}V_{1}  }{T_{1} } = \frac{P_{2}V_{2}  }{T_{2} }[/tex]

Given;

[tex]P_{1} = 0.43 atm\\ V_{1} =11.7 liters\\ T_{1} = ?[/tex]

While;

[tex]P_{2} = 3.61 atm\\ V_{2} =9.5 liters \\ T_{2} =627 K[/tex]

To calculate [tex]T_{1}[/tex]

[tex]T_{1} =\frac{P_{1}V_{1}T_{2}}{P_{2}V_{2}}[/tex]

[tex]T_{1} =\frac{(0.43 atm)(11.7 l)(627 K)}{(3.61 atm)(9.5 L)}[/tex]

               [tex]T_{1} =92.24 K[/tex]

Therefore the initial temperature is 92.24 K

Keywords: Combined gas laws, Boyle's law and Charles's law

Learn more about:

  • Boyles’s law: https://brainly.com/question/1158880
  • Gay-Lussac’s law: brainly.com/question/2438000
  • Charles’s law:brainly.com/question/2438000
  • Combined gas law: https://brainly.com/question/2441061

Level: High school

Subject: Chemistry

Topic: Gas laws

Sub-topic: Combined gas laws

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