Question

a balloon filled with helium gas at 20°c occupies 2.91 l at 1.00 atm. the balloon is immersed in liquid nitrogen at -196°c, raising the pressure to 5.20 atm. what is the volume of the balloon in the liquid nitrogen? a. 0.15 l b. 2.1 l c. 4.0 l d. 58 l e. 69 l

Explanation:

Step1: Convert temperatures to Kelvin

The formula for converting Celsius to Kelvin is \(T(K)=T(^{\circ}C)+273.15\).
For the initial temperature \(T_1 = 20^{\circ}C\), then \(T_1=20 + 273.15=293.15K\).
For the final temperature \(T_2=- 196^{\circ}C\), then \(T_2=-196 + 273.15 = 77.15K\).

Step2: Use the combined gas law

The combined gas law is \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\).
We are given \(P_1 = 1.00atm\), \(V_1=2.91L\), \(T_1 = 293.15K\), \(P_2 = 5.20atm\), \(T_2=77.15K\).
We need to solve for \(V_2\). Rearranging the combined - gas law formula gives \(V_2=\frac{P_1V_1T_2}{P_2T_1}\).
Substitute the values: \(V_2=\frac{1.00atm\times2.91L\times77.15K}{5.20atm\times293.15K}\).
First, calculate the numerator: \(1.00\times2.91\times77.15 = 224.5065\).
Then, calculate the denominator: \(5.20\times293.15=1524.38\).
Now, \(V_2=\frac{224.5065}{1524.38}\approx0.15L\).

Answer:

A. \(0.15L\)