Question

The reform reaction between steam and gaseous methane () produces "synthesis gas," a mixture of carbon monoxide gas and dihydrogen gas. Synthesis gas is one of the most widely used industrial chemicals, and is the major industrial source of hydrogen. Suppose a chemical engineer studying a new catalyst for the reform reaction finds that liters per second of methane are consumed when the reaction is run at and . Calculate the r

Answer 1

Complete Question:

The reform reaction between steam and gaseous methane (CH4) produces "synthesis gas," a mixture of carbon monoxide gas and dihydrogen gas. Synthesis gas is one of the most widely used industrial chemicals, and is the major industrial source of hydrogen.

Suppose a chemical engineer studying a new catalyst for the reform reaction finds that 924. liters per second of methane are consumed when the reaction is run at 261.°C and 0.96atm. Calculate the rate at which dihydrogen is being produced. Give your answer in kilograms per second. Round your answer to 2 significant digits.

Answer:

Rate at which H₂ is produced = 0.12 kg/s

Step-by-step explanation:

Volume of methane produced, V = 924 litres

Temperature, T = 261.°C = 261 + 273

T = 534 K

Pressure, P = 0.96 atm

Gas constant, R = 0.0821 L-atm/ K-mol

We will calculate the number of moles of methane used in the reaction.

`n_(methane) = (PV)/(RT) \\n_(methane) = (0.96 * 924)/(0.0821 * 534) \\n_(methane) = (887.04)/(43.8414)\\n_(methane) = 20.23 moles`

Equation of reaction:

`CH_(4) + H_(2) O \rightarrow CO + 3H_(2)`

From the reaction above :

1 mole of methane produced 3 moles of H₂

20.23 moles of methane will produce (20.23 * 3 ) moles of H₂

Number of moles of H₂,
`n_{H_(2) } = 60.69 moles`

That is 60.69 moles of hydrogen is produced per second.

Number of moles = Mass/ Molar mass

`n_{H_(2) } = \frac{Mass_{H_(2) }}{Molar mass_{H_(2) }} \\Mass_{H_(2)} = n_{H_(2) } * Molar mass_{H_(2) }\\Mass_{H_(2)} = 60.69 * 2.016\\Mass_{H_(2)} = 122.35 g`

Rate at which H₂ is produced = 122.35 g/s = 0.12 kg/s

Answer 2

The rate at which dihydrogen gas is being produced = 0.018 kg/s

Step-by-step explanation:

Firstly, we write the balanced equation for the production of the synthesis gas

CH₄ + H₂O → CO + 3H₂

The rate of consumption of CH₄ is 159 litres per second. With the reaction ran at T = 294°C and a pressure of 0.86 atm

Using the ideal gas equation, we can convert the volumetric rate of consumption of methane to molar rate of consumption

PV = nRT

PV' = n'RT

P = pressure = 0.86 atm = 87,139.5 Pa

V' = 159 L/s = 0.159 m³/s

n' = ?

R = molar gas constant = 8.314 J/mol.K

T = absolute temperature in Kelvin = 294°C = 567.15 K

87,139.5 × 0.159 = n' × 8.314 × 567.15

n' = (87,139.5 × 0.159) ÷ (8.314 × 567.15)

n' = 2.9383547773 mol/s = 2.938 mol/s

From the stoichiometry of this reaction,

1 mole of methane gives 3 moles of dihydrogen gas

2.938 mol/s of methane will correspond to (3 × 2.938) mol/s of dihydrogen gas, that is, 8.815 mol/s.

Mass flowrate = (molar flowrate) × (molar mass)

Molar flowrate = 8.815 mol/s

Molar mass of dihydrogen gas = 2 g/mol = 0.002 kg/mol

Mass flowrate = 8.815 × 0.002 = 0.0176301287 kg/s = 0.018 kg/s to 2 s.f.

Hope this Helps!!!