A balloon holds 29.3 kg of helium. What is the volume of the balloon if the final pressure is 1.2 atm and the temperature is 22°C?
using the equation pv=nrt would i put 29.3 kg in place of n? but n has to be in moles so how do you convert that?
thanks
29.3 kg = 29300 grams and moles = g/molar mass
To use the ideal gas equation, pv = nrt, you need to convert the mass of helium (29.3 kg) into moles. This requires using the molar mass of helium.
The molar mass of helium is approximately 4 g/mol, so you can calculate the number of moles using the following steps:
1. Convert the mass of helium from kilograms (kg) to grams (g):
29.3 kg × 1000 g/kg = 29300 g
2. Divide the mass in grams by the molar mass of helium:
29300 g ÷ 4 g/mol ≈ 7325 mol
Now you have the number of moles of helium (n), which is approximately 7325 mol.
Next, you can proceed to solve for the volume (V) of the balloon using the ideal gas equation:
pv = nrt
Given:
Pressure (p) = 1.2 atm
Temperature (T) = 22°C = 295 K (convert to Kelvin)
The gas constant (R) is 0.0821 L·atm/(mol·K).
Now you can rearrange the equation to solve for volume (V):
V = (nrt) / p
Substituting the known values:
V = (7325 mol × 0.0821 L·atm/(mol·K) × 295 K) / 1.2 atm
Calculating:
V ≈ 173,771.04 L
Therefore, the volume of the balloon is approximately 173,771.04 liters.