If you have a 578 g of fat (tristearin) stored in your body, how much heat will be produced when it is metabolized?
tristearin is C57H110O6
The chemical reaction:
C57H110O6(s) + O2(g) --> CO2(g) + H2O (l)
DHf:
C57H110O6(s) -390.70
O2(g) 0
CO2(g) -393.5
H2O(l) -285.840
I don't know how to figure this one out.
Balance the equation.
dHrxn = (n*dHf products) - (n*dHf reactants) in units of kJ/mol
q = dHrxn x (578/2*molar mass tristearin) = ?
-11385 J
I don't get that. The best way you can do this is to show the balanced equation, then show step by step what your math is like and I can find the error if you've made one. I think we're wasting time with your multiple answers and my no that isn't right.
-75520 (578 / 2(891.4468)g = -24483 J
Note here that you obtained 75520 for dHrxn but on page 1 you are not using half of that if you are doing for 1 mole. And the 75520 agrees with the number I had (before dividing by 2) for 1 mole.
Here, I obtained 890 for the molar mass but I used 12 for C, 16 for O and 1 for H. Those large numbers probably make the difference between 890 and 891.4468 Anyway, the set up is ok and the answer is ok.
To calculate the heat produced when tristearin is metabolized, you can use the concept of enthalpy change. The enthalpy change (ΔH) for a chemical reaction is the difference between the enthalpies of the products and the reactants.
In this case, the reaction is:
C57H110O6(s) + O2(g) → CO2(g) + H2O(l)
The enthalpy change (ΔH) for this reaction can be calculated by subtracting the sum of the enthalpies of the reactants from the sum of the enthalpies of the products:
ΔH = [Σ(ΔHf) products] - [Σ(ΔHf) reactants]
Substituting the given enthalpies of formation (ΔHf) values from your question:
ΔH = [ΔHf(CO2(g)) + ΔHf(H2O(l))] - [ΔHf(C57H110O6(s)) + ΔHf(O2(g))]
ΔH = [-393.5 + (-285.840)] - [-390.70 + 0]
ΔH = -678.34 - (-390.70)
ΔH = -678.34 + 390.70
ΔH = -287.64
The negative sign indicates that the reaction is exothermic, meaning it releases heat.
Now, to calculate the amount of heat produced when 578 g of tristearin is metabolized, you need to use the molar mass of tristearin.
The molar mass of tristearin (C57H110O6) can be calculated by adding up the atomic masses of carbon (C), hydrogen (H), and oxygen (O) in the molecule. You can find these values from the periodic table.
C: 12.01 g/mol
H: 1.01 g/mol
O: 16.00 g/mol
Molar mass of tristearin = (57 * 12.01) + (110 * 1.01) + (6 * 16.00) = 882.99 g/mol
Now, you can set up a proportion to calculate the heat produced when 578 g of tristearin is metabolized:
Heat produced (in kcal) / 882.99 g = ΔH (in kcal/mol) / 1 mol
You can rearrange this proportion to solve for the heat produced:
Heat produced (in kcal) = (578 g * ΔH) / 882.99 g
Substituting the value of ΔH (-287.64 kcal/mol) into the equation:
Heat produced (in kcal) = (578 g * -287.64 kcal/mol) / 882.99 g
Calculating this equation will give you the amount of heat produced when 578 g of tristearin is metabolized.