Question

a balloon is filled with 1.5 l of hydrogen at a temperature of 294 k and a pressure of 745 torr. at a high altitude of 20 km the temperature is 225 k and the pressure is 41.2 torr. what is the volume of the ballon at this altitude?
the combined gas law equation is seen below. match the value of each of the variables to its symbol in the equation. match the ? to the unknown variable.
based on the equation you set up in the previous activity, calculate the value of the unknown variable.
l

Explanation:

Step1: Identify the values of each variable

From the problem, we have:

• \(P_1 = 745\) torr (initial pressure)
• \(V_1=1.50\) L (initial volume)
• \(T_1 = 294\) K (initial temperature)
• \(P_2 = 41.2\) torr (final pressure)
• \(T_2=225\) K (final temperature)
• \(V_2\) is the unknown (final volume)

Step2: Rearrange the combined gas law formula \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\) to solve for \(V_2\)

$$V_2=\frac{P_1V_1T_2}{P_2T_1}$$

Step3: Substitute the values into the formula

$$V_2=\frac{745\times1.50\times225}{41.2\times294}$$

First, calculate the numerator: \(745\times1.50\times225 = 745\times337.5=251437.5\)

Then, calculate the denominator: \(41.2\times294 = 12112.8\)

Step4: Divide the numerator by the denominator

$$V_2=\frac{251437.5}{12112.8}\approx 20.76$$

Answer:

\(20.8\) L (rounded to one decimal place)