Answer:
The answer to your question is V2 = 4.97 l
Explanation:
Data
Volume 1 = V1 = 4.40 L Volume 2 =
Temperature 1 = T1 = 19°C Temperature 2 = T2 = 37°C
Pressure 1 = P1 = 783 mmHg Pressure 2 = 735 mmHg
Process
1.- Convert temperature to °K
T1 = 19 + 273 = 292°K
T2 = 37 + 273 = 310°K
2.- Use the combined gas law to solve this problem
P1V1/T1 = P2V2/T2
-Solve for V2
V2 = P1V1T2 / T1P2
-Substitution
V2 = (783 x 4.40 x 310) / (292 x 735)
-Simplification
V2 = 1068012 / 214620
-Result
V2 = 4.97 l
The final volume, in liters, of the gas is 4.98 L
From the question,
We are to determine the final volume of the gas.
Using the combined gas law formula,
[tex]\frac{P_{1}V_{1} }{T_{1}}= \frac{P_{2}V_{2}}{T_{2}}[/tex]
Where
P₁ is the initial pressure
V₁ is the initial volume
T₁ is the initial temperature
P₂ is the final pressure
V₂ is the final volume
and T₂ is the final temperature
From the given information
P₁ = 783 mmHg
V₁ = 4.40 L
T₁ = 19 °C = 273.15 + 19 = 292.15 K
P₂ = 735 mmHg
T₂ = 37 °C = 273.15 + 37 = 310.15 K
Putting the parameters into the formula, we get
[tex]\frac{783 \times 4.40}{292.15}= \frac{735 \times V_{2}}{310.15}[/tex]
Then,
[tex]V_{2} = \frac{783 \times 4.40 \times 310.15}{735 \times 292.15}[/tex]
[tex]V_{2} = \frac{1068528.78}{214730.25}[/tex]
[tex]V_{2} = 4.98 \ L[/tex]
Hence, the final volume, in liters, of the gas is 4.98 L
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