For the process
CH4(g) = C(s) + 2H2(g)
A reaction is started in a rigid vessel at 1000 K with 1 mole of methane and 1 mole of hydrogen gas at 10 bar. Use table C.3 from your text to determine how many grams of carbon should be formed after the reaction has reached equilibrium.
To determine the number of grams of carbon formed during the reaction, we need to calculate the number of moles of carbon formed at equilibrium, and then convert it to grams.
Step 1: Write the balanced chemical equation
The given reaction is:
CH4(g) = C(s) + 2H2(g)
Step 2: Determine the stoichiometry of the reaction
By looking at the balanced chemical equation, we can see that one mole of methane (CH4) reacts to form one mole of carbon (C). Therefore, the stoichiometric coefficient of carbon in the equation is 1.
Step 3: Determine the equilibrium conditions
The reaction is started in a rigid vessel at 1000 K with 1 mole of methane and 1 mole of hydrogen gas at 10 bar. We are interested in the equilibrium state of the reaction, which means that the reaction has reached a point where the concentrations of reactants and products remain constant.
Step 4: Use Table C.3 from your text to find the equilibrium constant (Kp)
Table C.3 provides the values of equilibrium constants at various temperatures. Look for the temperature closest to the given temperature of 1000 K. Once you find the appropriate temperature, note the equilibrium constant (Kp) for the given reaction.
Step 5: Calculate the number of moles of carbon at equilibrium
Since we know the stoichiometric coefficient of carbon in the reaction is 1, and the equilibrium constant (Kp), we can use the moles of methane at equilibrium to determine the moles of carbon at equilibrium.
Step 6: Convert moles of carbon to grams
To convert the moles of carbon to grams, we need to know the molar mass of carbon. Look up the molar mass of carbon from the periodic table. Once you have the molar mass, multiply it by the moles of carbon to get the mass in grams.
Note: The specific values for Kp, moles of methane at equilibrium, and molar mass of carbon will depend on the information provided in Table C.3 and the periodic table in your text.
Following these steps and referring to the provided resources, you should be able to determine how many grams of carbon should be formed after the reaction has reached equilibrium.
To determine the grams of carbon formed after the reaction has reached equilibrium, we need to calculate the number of moles of carbon formed and then convert it to grams.
Step 1: Write the balanced chemical equation for the reaction:
CH4(g) = C(s) + 2H2(g)
Step 2: Calculate the initial number of moles of each reactant:
1 mole of methane (CH4) and 1 mole of hydrogen gas (H2).
Step 3: Calculate the initial pressure of the system:
Given 10 bar pressure, which will remain constant throughout the reaction.
Step 4: Determine the value of the equilibrium constant, Kp, for the reaction:
Use table C.3 from your text to find the value of Kp at 1000 K for the reaction CH4(g) = C(s) + 2H2(g). Let's assume the value is 2.5 x 10^3 bar.
Step 5: Set up the equilibrium expression using the partial pressures:
Kp = (PC × PH2^2) / (PCH4)
Where PC is the partial pressure of carbon (C), PH2 is the partial pressure of hydrogen gas (H2), and PCH4 is the partial pressure of methane (CH4).
Step 6: Set up an ICE table to calculate the changes in partial pressures during the reaction:
Start with initial partial pressures (P0) and use stoichiometry to find the changes in pressure (ΔP).
Step 7: Calculate the "initial" partial pressure of carbon (PC) at equilibrium:
PC = P0 (change in pressure calculated in Step 6)
Step 8: Calculate the number of moles of carbon formed:
Moles of carbon = PC (initial partial pressure of carbon at equilibrium) / R (ideal gas constant) / T (temperature in Kelvin)
Since we are given pressure in bar, we need to convert it to Pascal units for the calculation.
Step 9: Convert the number of moles of carbon to grams:
Grams of carbon = Moles of carbon x molar mass of carbon
Note: Please refer to table C.3 from your text to accurately determine the equilibrium constant (Kp) at 1000 K for the reaction.