During an experiment, a student adds 0.339 g of calcium metal to 100.0 mL of 2.05 M HCl. The student observes a temperature increase of 11.0 °C for the solution. Assuming the solutions' final volume is 100.0 mL, the density is 1.00 g/mL, and the specific heat is 4.184 J/(g·°C), calculate the heat of the reaction, ΔHrxn.
q = mass H2O x specific heat H2O x delta T.
q give you the heat gained by the solution which is the heat of the reaction.
q/2.05 give heat in J/gram
(q/2.05)*40.08 gives delta H/mol.
I have a similar problem, but with different numbers. What did you end up getting for q?
To calculate the heat of the reaction (ΔHrxn), we can use the equation:
ΔHrxn = q / moles
where q is the amount of heat transferred and moles is the number of moles of the limiting reactant.
First, let's calculate the moles of calcium (Ca) by using its molar mass:
Molar mass of Ca = 40.08 g/mol
Mass of Ca = 0.339 g
moles of Ca = mass of Ca / molar mass of Ca
moles of Ca = 0.339 g / 40.08 g/mol
Next, we need to calculate the moles of hydrochloric acid (HCl) using its concentration:
Concentration of HCl = 2.05 M
Volume of HCl = 100.0 mL
moles of HCl = concentration of HCl * volume of HCl
moles of HCl = 2.05 M * 0.100 L
Since the balanced equation between Ca and HCl is 1:2, the moles of Ca will be divided by 2.
moles of Ca = (0.339 g / 40.08 g/mol) / 2
Now, let's calculate the heat transferred using the equation:
q = mcΔT
where:
m is the mass of the solution (density * volume)
c is the specific heat of the solution
ΔT is the change in temperature
Density = 1.00 g/mL
Volume = 100.0 mL
Mass of the solution = density * volume
Mass of the solution = 1.00 g/mL * 100.0 mL
ΔT = 11.0 °C
Now, we can calculate q:
q = (mass of the solution) * c * ΔT
Finally, we can calculate ΔHrxn using the equation:
ΔHrxn = q / moles of Ca
Let's calculate the values step by step:
1. Calculate moles of Ca:
moles of Ca = (0.339 g / 40.08 g/mol) / 2
2. Calculate the mass of the solution:
mass of the solution = 1.00 g/mL * 100.0 mL
3. Calculate q:
q = (mass of the solution) * c * ΔT
4. Calculate ΔHrxn:
ΔHrxn = q / moles of Ca
Let's plug in the values and calculate each step:
To calculate the heat of the reaction (ΔHrxn), we can use the equation:
ΔHrxn = q / n
where:
- ΔHrxn is the heat of the reaction
- q is the amount of heat transferred
- n is the number of moles of the limiting reactant
To calculate q, we need to use the equation:
q = m × c × ΔT
where:
- q is the amount of heat transferred
- m is the mass of the solution (in grams)
- c is the specific heat of the solution (in J/(g·°C))
- ΔT is the temperature change of the solution (in °C)
First, let's calculate the amount of heat transferred (q). We are given that the density of the solution is 1.00 g/mL, and the final volume is 100.0 mL. Therefore, the mass of the solution (m) can be calculated as:
m = density × volume
m = 1.00 g/mL × 100.0 mL
m = 100.0 g
Next, we can use the equation q = m × c × ΔT to calculate q. We are given ΔT = 11.0 °C and c = 4.184 J/(g·°C). Substituting these values into the equation:
q = 100.0 g × 4.184 J/(g·°C) × 11.0 °C
q ≈ 4593.44 J
Now, let's calculate the number of moles of calcium metal (n). We are given the mass of calcium metal added, which is 0.339 g. To calculate the number of moles, we need to divide the mass by the molar mass of calcium (40.08 g/mol):
n = mass / molar mass
n = 0.339 g / 40.08 g/mol
n ≈ 0.008459 mol
Finally, we can calculate the heat of the reaction (ΔHrxn) by dividing q by n:
ΔHrxn = 4593.44 J / 0.008459 mol
ΔHrxn ≈ 542,595 J/mol
So, the heat of the reaction (ΔHrxn) is approximately 542,595 J/mol.