consider the following reaction:
2CH3OH(g) yields 2CH4(g) + O2(g) change in enthalpy= 252.8kJ
How many kilojoules of heat are released when 38.4 g of CH_4 g) reacts completely with O2 (g) to form CH3OH (g) at constant pressure?
252.8 kJ x (38.4/2*molar mass CH4) = ?
247
To determine the amount of heat released when 38.4 g of CH4(g) reacts completely, we need to use the given reaction equation and the molar mass of CH4.
First, we'll calculate the number of moles of CH4:
Molar mass of CH4 = (1 * 12.01 g/mol) + (4 * 1.01 g/mol) = 16.04 g/mol
Number of moles of CH4 = (mass of CH4) / (molar mass of CH4)
Number of moles of CH4 = 38.4 g / 16.04 g/mol = 2.397 mol
Now, we can use the stoichiometry of the reaction to determine the number of moles of CH3OH produced:
From the balanced reaction: 2CH3OH(g) yields 2CH4(g) + O2(g)
We can see that for every 2 moles of CH4, 2 moles of CH3OH are produced.
Number of moles of CH3OH = (number of moles of CH4) / 2
Number of moles of CH3OH = 2.397 mol / 2 = 1.1985 mol
Next, we'll calculate the heat released per mole of CH3OH formed using the given change in enthalpy:
Heat released per mole of CH3OH = 252.8 kJ / 2 mol CH3OH
Finally, we can calculate the total heat released for 38.4 g of CH4 by multiplying the heat released per mole by the number of moles of CH3OH:
Total heat released = (Heat released per mole of CH3OH) * (number of moles of CH3OH)
Total heat released = (252.8 kJ/2 mol) * 1.1985 mol = 151.66 kJ
Therefore, approximately 151.66 kJ of heat are released when 38.4 g of CH4(g) reacts completely with O2(g) to form CH3OH(g) at constant pressure.
To determine the heat released during the reaction, we need to use the given enthalpy change value and the stoichiometry of the reaction. Here's how you can calculate it step by step:
1. First, we need to find the number of moles of CH4 (methane) in the given mass of 38.4 g.
The molar mass of CH4 is 16.04 g/mol (4*1.01 C + 4*1.01 H).
Number of moles = mass / molar mass
Number of moles of CH4 = 38.4 g / 16.04 g/mol ≈ 2.396 mol
2. Now that we know the number of moles of CH4, we can use the stoichiometry of the reaction to find the number of moles of CH3OH produced.
According to the balanced equation, 2 moles of CH4 produce 2 moles of CH3OH.
So, the number of moles of CH3OH produced = 2.396 mol * (2 mol CH3OH / 2 mol CH4) = 2.396 mol
3. Finally, we can calculate the heat released using the enthalpy change (∆H) value given in the question.
The enthalpy change is given as 252.8 kJ for 2 moles of CH4.
So, the heat released for 2.396 moles of CH4 can be calculated using a proportion:
Heat released (q) = (∆H * moles of CH4) / 2 mol CH4
q = (252.8 kJ * 2.396 mol) / 2 mol ≈ 604.29 kJ
Therefore, approximately 604.29 kJ of heat are released when 38.4 g of CH4 reacts completely with O2 to form CH3OH at constant pressure.