Question

A balloon filled with 50.3 L of He at 17.2°C and 1.00 atm rises to a height in the atmosphere where the pressure is 207 Torr and the temperature is − 32.4°C.
Part A) What is the final volume of the balloon? Assume that the pressure inside and outside the balloon have the same value Express your answer with the appropriate units.

Answer 1

Answer: The final volume of the balloon is 153 L

Explanation:

Combined gas law is the combination of Boyle's law, Charles's law and Gay-Lussac's law.

The combined gas equation is,

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

where,

$P_1$ = initial pressure of gas = 1.00 atm

$P_2$ = final pressure of gas = 207 torr = 0.272 atm      (760torr=1atm)

$V_1$ = initial volume of gas = 50.3 L

$V_2$ = final volume of gas = ?

$T_1$ = initial temperature of gas = $17.2^oC=273+17.2=290.2K$

$T_2$ = final temperature of gas = $-32.4^oC=273-32.4=240.6K$

Now put all the given values in the above equation, we get:

$\frac{1atm\times 50.3L}{290.2K}=\frac{0.272atm\times V_2}{240.6K}$

$V_2=153L$

Thus the final volume of the balloon is 153 L

Answer 2

Answer:

The final volume of the balloon is 153L

Explanation:

Step 1: Data given

Volume of He = 50.3 L

Temperature = 17.2 °C = 290.35 K

Pressure = 1.00 atm

The pressure rises to 207 torr =(207/760 = 0.2723684 atm)

The temperature lowers to -32.4°C = 240.75 K

What is the final volume of the balloon?

(P1*V1)/T1  = (P2*V2)/T2

⇒ with P1 = the initial pressure = 1.00 atm

⇒ with V1 = the initial volume = 50.3 L

⇒ with T1 = the initial temperature = 290.35 K

⇒ with P2 = the final pressure = 0.2723684 atm

⇒ with V2 = the final volume = TO BE DETERMINED

⇒ with T2 = the final temperature = 240.75 K

V2 = (P1 * V1 * T2) / (T1 * P2)

V2 = (1.00 * 50.3 * 240.75 K) / (290.35*0.2723684)

V2 = 153.1L ≈ 153L

The final volume of the balloon is 153 L