Answer to Question #253431 in General Chemistry for Jejemon

Question #253431

A balloon has a volume of 4.0L when at sea level(1.0atm)at a room temperature of 28°C.What will be its volume when inflated with the same amount of a gas at an elevation where the atmospheric pressure is 700 mmhg at 28°C


1
Expert's answer
2021-10-20T02:51:22-0400
"\\dfrac{P_1V_1}{T_1}=\\dfrac{P_2V_2}{T_2}=\\text{constant}"

The balloon has a volume of 4.0 L when at sea level (1.0 atm) at a room temperature of 28 °C.

"V_1=4.0\\ L=4\\times 10^{-3}\\ m^3,"

"P_1=1.0\\ atm=101325\\ Pa,"

"T_1=28\\degree C=(28+273)\\ K=301\\ K"

1mm Hg=133.322 Pa

"P_2=700mm\\ Hg=(700\\cdot 133.322)\\ Pa=93325.4\\ Pa"

 "T_2=28\\degree C=(28+273)\\ K=301\\ K=T_1"          




"\\dfrac{P_1V_1}{T_1}=\\dfrac{P_2V_2}{T_2}"

Solve for "V_2"



"V_2=\\dfrac{P_1T_1}{P_2T_2}V_1"


    


"V_2=\\dfrac{101325\\ Pa(301\\ K)}{93325.4\\ Pa(301\\ K)}\\cdot4\\times 10^{-3}\\ m^3""\\approx 4.343\\times 10^{-3}\\ m^3\\approx4.343\\ L"

The volume of gas will be "V_2=4.343\\ L."

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