Mg(s) + 2 HCl(aq) --> MgCl2(aq) + H2 (g) DeltaH= -4.6x10^2 kJ
How much heat is evolved when 0.598 g of Mg are dissolved in excess HCl?
I'm not sure how to go about this problem. What I thought to do was:
0.598 g x 1 mol Mg/24.31 g Mg x 2 mol HCl/ 1 mol Mg x 36.46 g HCl/ 1 mol HCl = 1.79 g HCl
and from here I am not sure what to do. Somehow I need to incorporate the DeltaH into a formula, I believe.
Your approach is to perform a stoichiometry calculation to find the grams HCl but that isn't what the problem is asking. Try something like this.
You know dissolving 1 mole Mg (24.3 g) in HCl produces 4.6E2 kJ. So how much heat will just 0.598 g Mg evolve?
That will be
4.6E2 kJ x 0.598/24.3 = ??
So the grams must cancel each other out when we divide and it leaves us with just kJ? So -11.3 kJ
Yes, but I notice there are only two significant figures in 4.6E2; therefore, the answer should not contain more than two. I would round 11.3 kJ to 11 kJ energy released (-11 kJ for delta H).
Oh that's right, thank you!
To solve this problem, you need to use the given values and the concept of stoichiometry to calculate the amount of heat evolved. Here's how you can proceed:
1. Calculate the number of moles of Mg using its molar mass:
Number of moles of Mg = Mass of Mg / Molar mass of Mg
Number of moles of Mg = 0.598 g / 24.31 g/mol ≈ 0.0246 mol
2. Use the balanced chemical equation to determine the stoichiometry between Mg and HCl. From the equation, you can see that 1 mole of Mg reacts with 2 moles of HCl.
3. Calculate the number of moles of HCl that react with the given amount of Mg:
Number of moles of HCl = Number of moles of Mg × (2 moles of HCl / 1 mole of Mg)
Number of moles of HCl = 0.0246 mol × (2 mol HCl / 1 mol Mg) ≈ 0.0493 mol
4. Now, calculate the amount of heat evolved using the given value of ΔH:
Heat evolved = ΔH × Number of moles of HCl
Heat evolved = (-4.6 × 10^2 kJ) × 0.0493 mol ≈ -22.598 kJ
Note: The negative sign in the value indicates that the reaction is exothermic, meaning it releases heat.
So, when 0.598 g of Mg is dissolved in excess HCl, approximately -22.598 kJ of heat is evolved.