A typical party balloon when inflated has a volume of 7.3 L. How many moles of helium are in the balloon if the pressure of helium is 1.2 atm and the temperature is 20.7 °C? Take the value of R to be 0.08206 L-atm/mol-K.
To calculate the number of moles of helium in the balloon, we can use the ideal gas law equation, which states:
PV = nRT
where:
- P represents the pressure of the gas (in atm)
- V represents the volume of the gas (in liters)
- n represents the number of moles of the gas
- R is the ideal gas constant (0.08206 L-atm/mol-K)
- T represents the temperature of the gas (in Kelvin)
We can rearrange the equation to solve for the number of moles:
n = (PV) / (RT)
Let's plug in the given values into the equation:
P = 1.2 atm
V = 7.3 L
R = 0.08206 L-atm/mol-K
T = 20.7 + 273.15 K (to convert Celsius to Kelvin)
Using these values, we can calculate the number of moles of helium:
n = (1.2 atm * 7.3 L) / (0.08206 L-atm/mol-K * (20.7 + 273.15) K)
n ≈ 0.3706 moles
Therefore, there are approximately 0.3706 moles of helium in the balloon.
To find the number of moles of helium in the balloon, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in liters)
n = number of moles of gas
R = ideal gas constant (0.08206 L-atm/mol-K)
T = temperature of the gas (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 20.7 °C + 273.15 K
T(K) = 293.25 K
Now we can rearrange the ideal gas law equation to solve for the number of moles:
n = (PV) / (RT)
Substituting the given values:
n = (1.2 atm * 7.3 L) / (0.08206 L-atm/mol-K * 293.25 K)
Calculating:
n = 0.983 moles
Therefore, there are approximately 0.983 moles of helium in the balloon.
Use PV = nRT
Remember T must be in kelvin.