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 rate at which dihydrogen is being produced. Give your answer in kilograms per second
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.8887
To calculate the rate at which dihydrogen is being produced, we need to convert the given information into appropriate units and apply stoichiometric calculations.
Let's start by converting 50 liters per second of methane to moles.
1. We know that the molar volume of gas at standard conditions (0°C and 1 atm pressure) is 22.4 liters per mole. Therefore, we can calculate the volume of methane consumed in moles.
Volume (in liters) of methane consumed = 50 liters/second
Moles of methane consumed = (50 liters/second) / (22.4 liters/mole)
= 2.23 moles/second
Next, we need to determine the stoichiometry of the reaction. The balanced equation for the reform reaction between methane (CH4) and steam (H2O) is as follows:
CH4 + H2O → CO + 3H2
From the equation, we can see that for every 1 mole of methane consumed, 3 moles of dihydrogen are produced. Thus, the rate at which dihydrogen is being produced is given by:
Moles of dihydrogen produced = 3 × moles of methane consumed
= 3 × 2.23 moles/second
= 6.69 moles/second
Finally, we need to convert the moles of dihydrogen produced to kilograms per second. To do this, we'll use the molar mass of hydrogen, which is approximately 2 grams/mole.
Mass of dihydrogen produced = Moles of dihydrogen produced × molar mass of hydrogen
= 6.69 moles/second × 2 grams/mole
= 13.38 grams/second
To convert grams to kilograms, divide by 1000:
Mass of dihydrogen produced = 13.38 grams/second ÷ 1000
= 0.01338 kilograms/second
Therefore, the rate at which dihydrogen is being produced is approximately 0.01338 kilograms per second.
To calculate the rate at which dihydrogen is being produced, we need to use the stoichiometry of the given reaction and the molar masses of the compounds involved.
Given:
- The volume flow rate of methane consumed = liters per second.
- The temperature and pressure of the reaction conditions are not provided. However, if we assume standard temperature and pressure (STP), the value for temperature would be 273.15 K (0°C) and the value for pressure would be 1 atmosphere (atm).
The balanced reform reaction equation is as follows:
CH4 (g) + H2O (g) -> CO (g) + 3H2 (g)
From the balanced equation, we can see that one mole of methane reacts to produce three moles of dihydrogen. However, we are given the volume flow rate of methane, not the concentration or number of moles. Thus, to find the number of moles of methane reacted, we need to convert the volume flow rate to moles.
To convert the volume flow rate of methane to moles, we need to know the temperature and pressure of the reaction. As these values are not provided, we will assume STP conditions for simplicity.
At STP (0°C, 1 atm), 1 mole of any ideal gas occupies 22.4 liters. Therefore, we can convert the volume flow rate of methane to moles using the following equation:
moles of methane = liters of methane / 22.4
Now, let's calculate the moles of methane reacted and then determine the moles of dihydrogen produced:
Moles of methane = liters per second / 22.4
To find the moles of dihydrogen produced, we multiply the number of moles of methane by the stoichiometric coefficient of dihydrogen, which is 3:
Moles of dihydrogen = Moles of methane * 3
To convert the moles of dihydrogen to kilograms, we need to know the molar mass of dihydrogen. The molar mass of hydrogen is approximately 2 grams per mole (g/mol).
Molar mass of dihydrogen = 2 g/mol
To convert moles to kilograms, we multiply by the molar mass and divide by 1000:
Mass of dihydrogen = Moles of dihydrogen * Molar mass of dihydrogen / 1000
Finally, to calculate the rate at which dihydrogen is being produced in kilograms per second, we need to divide the mass of dihydrogen by the time:
Rate of dihydrogen production = Mass of dihydrogen / Time
Make sure to substitute the given values into the appropriate equations and units for an accurate result.