Question

Hydrogen can be extracted from natural gas according to the following reaction:

Answer 1

Answer:

There will be produced 379 grams of H2

The percent yield under these conditions is 7.45 %

Explanation:

Step 1: The balanced equation

CH4(g)+CO2(g) → 2CO(g)+2H2(g)

Step 2: Given data

Kp = 4.5*10²

Temperature = 825 Kelvin

Volume = 85.0 L

Mass of CH4 = 22.3 Kg

Mass of CO2 = 55.4 Kg

Molar mass of CH4 = 16.04 g/mole

Molar mass of CO2 = 44.01 g/mole

Step 3: Calculate moles of CH4

moles of CH4 = mass of CH4 / Molar mass of CH4

moles of CH4 = 22300 / 16.04 = 1390.3

Step 4: Calculate moles of CO2

moles of CO2 = mass of CO2 / Molar mass of CO2

moles of CO2 = 55400 / 44.01 = 1258.80 moles

Step 5: Calculate moles of H2

For 1 mole of CH4 we need 1 mole of CO2 to produce 2 moles of H2

so there will be produced 2*1258.8 = 2517.6 moles of H2

Step 6: Calculate theoretical mass of H2

mass of H2 = Number of moles of H2 * Molar mass of H2

mass of H2 = 2517.6 moles *2.02 g/mole = 5085.552 grams

Step 7: Calculate pressure of CH4

P*V = n*R*T

P =(n*R*T) / V

P = 1390.3*.0821*825/85 = 1107.86atm

Step 8: Calculate pressure of CO2

P*V = n*R*T

P =(n*R*T) / V

P = 1258.80*.0821*825/85 = 1003.08atm

Step 9

Kp= 4.5 *100 =[P(H2)^2 * P(CO)^2]/[P(CO2) * P(CH4)]

450=16X^4/[(1107.86-X)(1003.08-X)]

450=16X^4/[(1107.86)(1003.08)]

(1107.86)(1003.08)*450=16X^4

X = 74.77

We plug this value in for "X" in the ICE chart. Only H2 since thats what the problem wants.

for H2 (2 moles) so 2X = 2*74.77 = 149.54

Step 10: Calculate number of moles of H2

n = P*V/ R*T

n = (149.54 *85 )/(0.0821 * 825) = 187.66 moles H2

Step 11: Calculate mass of H2

mass of H2 = Number of moles H2 * Molar mass of H2

mass of H2 = 187.66 * 2.02 g/moles = 379.07 grams H2 ≈ 379 grams of H2

Step 12: Calculate the yield

(379 grams of H2 / 5085.552 grams of H2 ) * 100 % = 7.45 %

The percent yield under these conditions is 7.45 %