When 0.638 g of Ca metal is added to 200.0 mL of 0.500 M HCl(aq), a temperature increase of 104C is observed.

Assume the solution's final volume is 200.0 mL, the density is 1.00 g/mL, and the heat capacity is 4.184 J/gC.

The molar heat of reaction for the reaction of Ca(s) + 2H^+(aq) Ca^2+(aq) + H2(g)is _____kJ/mol.

Mass H2O x specific heat x delta T = q = heat evolved when 0.638 g Ca is reacted with HCl.

So q/0.638 will give you J/g
Convert that to J/mol.
Post your work if you get stuck.

Mass H2O x specific heat x delta T = q

200 g x [(4.184 J/gC)/18.02g] x 10.4 C = q
482.928 = q

q/0.638 --> 482.928/0.638 = 756.972 J/g

Is that right so far?

To find the molar heat of reaction, we first need to calculate the amount of heat released or absorbed during the reaction.

We can use the equation:

q = m * C * ΔT

where q is the heat released or absorbed, m is the mass of the solution, C is the heat capacity, and ΔT is the change in temperature.

Given:
Mass of Ca metal (m) = 0.638 g
Volume of HCl solution (V) = 200.0 mL
Concentration of HCl (C) = 0.500 M
Temperature increase (ΔT) = 104 °C
Heat capacity (C) = 4.184 J/g°C

First, let's convert the volume of the HCl solution from milliliters to grams using the density:

Volume (V) = 200.0 mL = 200.0 g

Next, we need to calculate the moles of HCl reacted. Since the molar ratio between Ca and HCl is 1:2, the number of moles of HCl is twice the number of moles of Ca.

Moles of Ca (n) = mass/molar mass = 0.638 g / (40.08 g/mol) = 0.0159 mol
Moles of HCl (n) = 2 * 0.0159 mol = 0.0318 mol

Now, we can calculate the amount of heat released or absorbed during the reaction:

q = m * C * ΔT = (200.0 g) * (4.184 J/g°C) * (104 °C) = 869,248 J

Finally, we can calculate the molar heat of reaction using the equation:

Molar heat of reaction = q/n

Molar heat of reaction = (869,248 J) / (0.0318 mol) = 27,309,748 J/mol

To convert J/mol to kJ/mol, divide the result by 1000:

Molar heat of reaction = 27,309,748 J/mol / 1000 = 27,310 kJ/mol

Therefore, the molar heat of reaction for the reaction of Ca(s) + 2H+(aq) → Ca^2+(aq) + H2(g) is 27,310 kJ/mol.