Given the following reaction that has an enthalpy of +128 kJ.
CH3OH(l) ---> CO(g) + 2H2(g)
How many kJ of heat are consumed when 50.1 g of CH3OH(l) reacts as shown in the equation?
So your reaction tells you that 128 kJ is consumed when 1 mol (32 g CH3OH) is used. You want to know for 50.1 so that is
128 kJ x (50.1/32) = ? kJ
To find out how many kJ of heat are consumed when 50.1 g of CH3OH(l) reacts, you need to use the following equation:
q = m * ΔH
where:
q is the heat consumed or released (in kJ)
m is the mass of CH3OH(l) (in grams)
ΔH is the enthalpy change for the reaction (in kJ)
First, you need to calculate the number of moles of CH3OH(l) using its molar mass. The molar mass of CH3OH (methanol) is approximately 32.04 g/mol.
moles of CH3OH = mass of CH3OH / molar mass of CH3OH
= 50.1 g / 32.04 g/mol
= 1.563 mol
The molar ratio between CH3OH and the products CO and H2 is 1:1:2, meaning that 1 mole of CH3OH produces 1 mole of CO and 2 moles of H2.
Therefore, the number of moles of CO produced is also 1.563 mol, and the number of moles of H2 produced is twice that, or 3.126 mol.
Now, you can calculate the heat consumed using the given enthalpy change of +128 kJ:
q = m * ΔH
= 1.563 mol * 128 kJ/mol
= 199.904 kJ
Therefore, 50.1 g of CH3OH(l) reacts, consuming approximately 199.904 kJ of heat.
To find how many kJ of heat are consumed when 50.1 g of CH3OH(l) reacts, you need to use the equation's enthalpy value, as well as the molar mass of CH3OH.
Here's the step-by-step process to solve the problem:
1. Calculate the molar mass of CH3OH. This can be done by adding up the atomic masses of the constituent elements. The molar mass of carbon (C) is 12.01 g/mol, hydrogen (H) is 1.01 g/mol, and oxygen (O) is 16.00 g/mol. Therefore, the molar mass of CH3OH is:
(1 * 12.01 g/mol) + (4 * 1.01 g/mol) + (1 * 16.00 g/mol) = 32.04 g/mol
2. Determine the number of moles of CH3OH using the mass and molar mass. Since you have 50.1 g of CH3OH, divide the given mass by the molar mass:
50.1 g / 32.04 g/mol = 1.563 mol
3. Finally, calculate the heat consumed using the stoichiometry of the balanced equation and the enthalpy change value provided:
1 mole of CH3OH reacts to produce +128 kJ of heat.
Since 1.563 moles of CH3OH will be consumed, multiply the moles by the enthalpy change:
1.563 mol * 128 kJ/mol = 200.064 kJ
Therefore, approximately 200.1 kJ of heat are consumed when 50.1 g of CH3OH reacts.