Hydrogen holds promise as an environment friendly fuel. How many grams of H2 gas are present in a 52.0 L fuel tank at a pressure of 2861 lb/in2 (psi) at 20.0°C? Assume that 1 atm = 14.7 psi.
To find the number of grams of H2 gas in the fuel tank, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the pressure from psi to atm:
2861 lb/in^2 * (1 atm/14.7 psi) = 194.90 atm
Next, we need to convert the volume from liters to moles. We'll use the ideal gas law equation again:
n = PV / RT
n = (194.90 atm * 52.0 L) / (0.0821 L·atm/(mol·K) * (20.0 + 273.15) K)
n ≈ 206.61 mol
Finally, we'll convert moles to grams using the molar mass of hydrogen (H2):
molar mass of H2 = 2.02 g/mol
Mass of H2 gas = n * molar mass of H2
Mass of H2 gas = 206.61 mol * 2.02 g/mol
Mass of H2 gas ≈ 417.72 g
Therefore, there are approximately 417.72 grams of H2 gas in the 52.0 L fuel tank at a pressure of 2861 lb/in^2 (psi) at 20.0°C.
To determine the mass of hydrogen gas present in the fuel tank, we need to use the Ideal Gas Law equation: PV = nRT.
First, we need to convert the given pressure from pounds per square inch (psi) to atmospheres (atm). Since 1 atm is equal to 14.7 psi, we can divide the given pressure of 2861 psi by 14.7 psi/atm to get the pressure in atmospheres: 2861 psi / 14.7 psi/atm = 194.9 atm.
Next, we convert the temperature from Celsius to Kelvin by adding 273.15 to the given value: 20.0°C + 273.15 = 293.15 K.
The Ideal Gas Law equation can be rearranged to solve for the number of moles (n) of gas:
n = PV / RT
Where:
P = pressure (in atm)
V = volume (in liters)
R = Ideal Gas Constant (0.0821 L∙atm/(mol∙K))
T = temperature (in Kelvin)
Now we can substitute the values into the equation:
n = (194.9 atm) x (52.0 L) / [(0.0821 L∙atm/(mol∙K)) x (293.15 K)]
Simplifying the equation gives us:
n = 4081.48 mol
Since 1 mole of H2 gas is equal to 2 grams, we can calculate the mass of the hydrogen gas:
mass of H2 gas = (4081.48 mol) x (2 g/mol) = 8162.96 g
Therefore, there are approximately 8162.96 grams of H2 gas present in the 52.0 L fuel tank at a pressure of 2861 lb/in2 (psi) and a temperature of 20.0°C.
PV=nRT=grams*RT/2
grams= 2*PV/RT
change pressure to 2861*101.4/14.7 kpa
change temp to kelvins
then compute grams, using the appropriate R