Calculate the pressure of 0.800 moles of helium gas, when the gas is in a balloon with a volume of 2.30 L at a temperature of 32°C.
PV = nRT
To calculate the pressure of a gas using the ideal gas law, you need to use the following equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant
T is the temperature of the gas in Kelvin
In this case, we are given:
n = 0.800 moles
V = 2.30 L
T = 32°C
First, we need to convert the temperature from Celsius to Kelvin. The Kelvin scale is an absolute temperature scale where 0 K is absolute zero, which is equivalent to -273.15°C.
To convert Celsius to Kelvin, you add 273.15 to the Celsius value.
So, T = 32°C + 273.15 = 305.15 K
Next, we need the value for the ideal gas constant, R. The ideal gas constant is typically given as 0.0821 L·atm/(mol·K). However, be careful to check if the units of the other quantities you have match the units of the gas constant.
Plugging the values into the ideal gas law equation, we have:
PV = nRT
P * 2.30 L = 0.800 mol * (0.0821 L·atm/(mol·K)) * 305.15 K
Now, we can solve for P by dividing both sides of the equation by 2.30 L:
P = (0.800 mol * 0.0821 L·atm/(mol·K) * 305.15 K) / 2.30 L
P ≈ 27.6 atm
So, the pressure of 0.800 moles of helium gas in a balloon with a volume of 2.30 L at a temperature of 32°C is approximately 27.6 atm.