Question

1. A weather balloon is filled with helium on a cool morning when the temperature is 13.0°C. The temperature is predicted to reach 35.0°C around 4 PM. When first inflated, the balloon has a volume of 12.9 L and is at 238 kPa – these are the standard volume and pressure for this type of weather balloon. Based on the balloon design, it can only withstand pressures up to 252 kPa.
How many moles of helium are in this hot air balloon?
Will the balloon burst when the temperature reaches 35.0 C?

Please someone help, Im mostly stumped by R. I know it is 8.314 L kPa/mole K but i dont know how to calculate that please help

Answer 1

Answer:

Number of moles: n = 1.29 moles

If the temperature reaches 35°C which is 308.15 K the balloon will burst

Explanation:

Using the formula: PV = nRT  

Where P is pressure in atm, V is volume in L, n is the number of moles, R is the gas constant which can be 8.314 J/mol K or 0.08206 atm L/mol K, and T is temperature in K.

In order to know which R to use, just take a look at the units. If you are given the pressure in atm, then use 0.08206 atm L/mol K. If you are given energy in Joules instead, then use 8.314 J/mol K.

Problem solution:

1 atm = 101.325 kPa, so 238 kPa is equal to 2.349 atm

1°C is 274.15 K, so 13°C is 286.15 k

Using the formula PV = nRT

2.349 atm * 12.9 L = n * 0.08206 atm L/mol K * 286.15 k  

n = (30.302 atm L) / (23.481 atm L/mol)

n = 1.29 moles

If the temperature reaches 35°C which is 308.15 K the balloon will burst:

P = nRT/V

P = (1.29 moles * 0.08206 atm L/mol K * 308.15 k) / 12.9 L

P = 2.529 atm = 256.21 kPa