Respuesta :
Answer:
New volume V2 = 92.7 Liter (Approx)
Explanation:
Given:
V1 = 106 l
T1 = 45 + 273.15 = 318.15 K
P1 = 740 mm
T2 = 20 + 273.15 = 293.15 K
P2 = 780 mm
Find:
New volume V2
Computation:
P1V1 / T1 = P2V2 / T2
(740)(106) / (318.15) = (780)(V2) / (293.15)
New volume V2 = 92.7 Liter (Approx)
The final volume will be 44.69 L
Initial volume V₁ = 106.0 L
Initial pressure P₁ = 740.0 mm of Hg
Initial temperature T₁ = 45.0⁰C
Final pressure P₂ = 780.0 mm of Hg
Final temperature T₂ = 20.0⁰C
It is required to calculate the final volume V₂
What is an ideal gas equation?
The ideal gas equation is formulated as:
PV = nRT.
In this equation, P refers to the pressure of the ideal gas, V is the volume of the ideal gas, n is the total amount of ideal gas that is measured in terms of moles, R is the universal gas constant, and T is the temperature.
Applying the ideal gas equation considering the gas inside the balloon to be ideal, to get the new volume.
So, from ideal gas law, we get,
[tex]\frac{PV}{T} = constant[/tex]
where P = pressure, V= Volume, T= temperature.
So,
[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]
[tex]V_2 = \frac{P_1V_1T_2}{P_2T_1}[/tex]
On substituting the values;
[tex]V_2=\frac{106.0\times740.0\times20.0}{780.0\times45}[/tex]
V₂ = 44.69 L
Hence, The final volume will be 44.69 L
To learn more about ideal gas equation, click here:
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