What is the total pressure in atmospheres of a 5.0 liter balloon containing 0.3 mol of helium, 0.2 mol of argon, and 0.5 mol of hydrogen gas at a temperature of 35°C?
To calculate the total pressure in atmospheres, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
So, T(K) = 35 + 273.15 = 308.15 K
Next, we need to calculate the total number of moles. Since we have different gases in the balloon, we need to add up the number of moles for each gas:
Total moles = moles of helium + moles of argon + moles of hydrogen
Total moles = 0.3 mol + 0.2 mol + 0.5 mol
Total moles = 1.0 mol
Now, we can substitute the values into the ideal gas law equation:
PV = nRT
P * 5.0 L = 1.0 mol * 0.0821 L·atm/mol·K * 308.15 K
P * 5.0 L = 25.25 L·atm
Divide both sides by 5.0 L:
P = 25.25 L·atm / 5.0 L
P = 5.05 atm
Therefore, the total pressure in atmospheres of the 5.0 liter balloon is 5.05 atm.