Hi, quick question:
Graphite is burned in oxygen to give carbon monoxide and carbon dioxide. If the product mixture is 33% CO and 67% CO2 by mass, what is the heat from the combustion of 1.00 g of graphite?
dH values:
CO:-110.5 kj/mol, CO2: -393.5 kj/mol
Thanks!
To find the heat from the combustion of 1.00 g of graphite, we need to calculate the amount of CO and CO2 produced and then determine the total heat released.
Let's start by finding the moles of CO and CO2 produced:
1. Convert the mass of graphite to moles:
We know that the molar mass of graphite is 12.01 g/mol. So, we can divide the given mass of graphite (1.00 g) by the molar mass of graphite to find the moles of graphite burned.
Number of moles of graphite = Mass of graphite / Molar mass of graphite
Number of moles of graphite = 1.00 g / 12.01 g/mol
2. Determine the moles of CO and CO2 produced using the given mass percentages:
We are given that the product mixture is 33% CO and 67% CO2 by mass.
Mass of CO = 33% * Total mass of products
Mass of CO2 = 67% * Total mass of products
To find the total mass of products, we can use the mass of the graphite.
Total mass of products = Mass of graphite + Mass of CO + Mass of CO2
Total mass of products = 1.00 g + Mass of CO + Mass of CO2
Now, we have two equations:
Mass of CO = 33% * (1.00 g + Mass of CO + Mass of CO2)
Mass of CO2 = 67% * (1.00 g + Mass of CO + Mass of CO2)
To simplify, let's assign 'x' to Mass of CO and 'y' to Mass of CO2.
Mass of CO = 0.33 * (1.00 g + x + y)
Mass of CO2 = 0.67 * (1.00 g + x + y)
3. Convert the masses of CO and CO2 to moles:
Now, we can convert the masses of CO and CO2 into moles using their respective molar masses.
Moles of CO = Mass of CO / Molar mass of CO
Moles of CO2 = Mass of CO2 / Molar mass of CO2
4. Use the coefficients in the balanced equation:
The balanced equation for the combustion of graphite is:
C(graphite) + O2 → CO + CO2
From the balanced equation, we can see that the ratio of moles of CO to moles of CO2 is 1:1.
Therefore, the moles of CO and CO2 are equal:
Moles of CO = Moles of CO2
Now, we can equate the expressions for the moles of CO and CO2 from steps 2 and 3:
Mass of CO / Molar mass of CO = Mass of CO2 / Molar mass of CO2
Substituting the expressions for Mass of CO and Mass of CO2, we have:
0.33 * (1.00 g + x + y) / Molar mass of CO = 0.67 * (1.00 g + x + y) / Molar mass of CO2
5. Solve for x and y:
Now, we can solve the equation to find the values of x and y.
0.33 * (1.00 g + x + y) / Molar mass of CO = 0.67 * (1.00 g + x + y) / Molar mass of CO2
Cross-multiply and solve for x and y:
0.33 * (1.00 g + x + y) * Molar mass of CO2 = 0.67 * (1.00 g + x + y) * Molar mass of CO
0.33 * Molar mass of CO2 + 0.33 * Molar mass of CO2 * x + 0.33 * Molar mass of CO2 * y = 0.67 * Molar mass of CO + 0.67 * Molar mass of CO * x + 0.67 * Molar mass of CO * y
Rearranging the equation:
(0.33 * Molar mass of CO2 - 0.67 * Molar mass of CO) * x + (0.33 * Molar mass of CO2 - 0.67 * Molar mass of CO) * y = 0.67 * Molar mass of CO - 0.33 * Molar mass of CO2
Now, we can calculate the values of x and y.
6. Calculate the heat released:
Now that we have the moles of CO and CO2 produced, we can calculate the heat released during the combustion of 1.00 g of graphite.
Heat released = Moles of CO * ΔH of CO + Moles of CO2 * ΔH of CO2
Substitute the values for the moles of CO and CO2, as well as the given ΔH values:
Heat released = (Moles of CO) * (-110.5 kJ/mol) + (Moles of CO2) * (-393.5 kJ/mol)
Calculate the final value to find the heat released.