When 0.667 g of Ca metal is added to 200.0 mL of 0.500 M HCl(aq), a temperature increase of 108C 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. what is the molar heat of reaction, H rxn, for the reaction of
Ca(s) + 2H+(aq) =Ca2+(aq) + H2(g) in kj/mol
do i use the same concept
mass water x specific heat water x delta T = q
how do i find mass water and specific heat water though
yes.
density of water is 1.00 g/mL (given) so 200 mL has a mass of 200 grams.
specific heat water = 4.184 J/g*C.
To calculate the molar heat of reaction, H_rxn, for the given chemical reaction, you cannot directly use the concept of "mass water x specific heat water x delta T = q" because there is no direct involvement of water in this reaction.
Instead, you need to use the concept of calorimetry to solve this problem. Calorimetry involves measuring the heat changes in a system during a chemical reaction or physical process.
Here's how you can approach this problem step by step:
1. Determine the heat, q, released by the reaction using the temperature increase (∆T) and the heat capacity (C) of the solution. The formula to calculate heat is q = C × ∆T.
In this case, the temperature increase (∆T) is given as 108 °C, and the heat capacity (C) is given as 4.184 J/g°C. However, for ease of calculations, you need to convert the mass of calcium, 0.667 g, to grams using its density (1.00 g/mL) since the specific heat is given in J/g°C.
So, q = C × ∆T = (4.184 J/g°C) × (0.667 g) × (108 °C).
2. Determine the moles of calcium used in the reaction. Since the balanced equation tells us that the reaction involves 1 mole of calcium, Ca(s), for every mole of reacted molecules, you assume that the moles of Ca used are the same as the moles of Ca2+ formed.
You can use the given concentration (0.500 M) and volume (200.0 mL, converted to L) of the hydrochloric acid solution to calculate the moles of H+ present in the solution using the formula: moles = concentration × volume.
Moles of Ca used = Moles of H+ = 0.500 M × (200.0 mL / 1000 mL/L).
3. Calculate the molar heat of reaction, H_rxn. The molar heat of reaction is defined as the heat change per mole of the limiting reactant (in this case, Ca metal). So, you need to divide the heat (q) from step 1 by the moles of Ca used from step 2.
H_rxn = q / moles of Ca used.
4. Finally, to express the molar heat of reaction in kJ/mol, you can convert the heat (q) from joules to kilojoules by dividing it by 1000, and divide the result by the moles of Ca used to get the molar heat of reaction in kJ/mol.
Remember to follow proper unit conversions throughout the calculations to ensure correct results.
I hope this explanation helps you understand how to solve the problem.