On a summer day early in the morning, a balloon is filled with helium when the temperature is 19°C, but the temperature will reach a peak of 42°C later in the day. The balloon holds 11.4 L of helium gas at a starting pressure of 239 kPa. The balloon will burst when the internal pressure reaches 256 kPa. Answer the following questions and show your work.
How many moles of helium gas are in the balloon?
What will the gas pressure be in the balloon at the peak temperature?
Will the balloon burst when the temperature reaches 42°C? Explain.
To solve these questions, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in kPa)
V = volume (in L)
n = number of moles
R = ideal gas constant (8.31 L∙kPa/mol∙K)
T = temperature (in Kelvin)
1. How many moles of helium gas are in the balloon?
Given:
P = 239 kPa
V = 11.4 L
T = 19°C = 19 + 273 = 292 K
Using the ideal gas law, we can solve for n:
239 kPa * 11.4 L = n * (8.31 L∙kPa/mol∙K) * 292 K
n = (239 kPa * 11.4 L) / (8.31 L∙kPa/mol∙292 K)
n ≈ 11.6 moles
Therefore, there are approximately 11.6 moles of helium gas in the balloon.
2. What will the gas pressure be in the balloon at the peak temperature?
Now at the peak temperature, the temperature is 42°C = 42 + 273 = 315 K. We can use the ideal gas law again to solve for the pressure:
P = nRT / V
P = 11.6 mol * (8.31 L∙kPa/mol∙K) * 315 K / 11.4 L
P ≈ 224 kPa
Therefore, the gas pressure in the balloon at the peak temperature will be approximately 224 kPa.
3. Will the balloon burst when the temperature reaches 42°C? Explain.
No, the balloon will not burst when the temperature reaches 42°C. The balloon will burst when the internal pressure reaches 256 kPa, and since the pressure at the peak temperature is only 224 kPa, it is below the burst pressure of 256 kPa.