When 10.00 mL of 1.00 M HCl solution is mixed with 115 mL of 0.100 M NaOH solution in a constant-pressure calorimeter, the temperature rises from 22.45 °C to 23.25 °C. Calculate q for this reaction, assuming that the heat capacity of the calorimeter is the same as that of 125 g of water.
To calculate the heat of the reaction (q), we can use the equation:
q = m * s * ΔT
Where:
q = heat of the reaction
m = mass of the solution (in this case, the sum of HCl and NaOH solutions)
s = specific heat capacity of the solution
ΔT = change in temperature
First, we need to determine the mass of the solution. We can do this by adding the masses of the HCl and NaOH solutions together.
Mass of HCl solution = volume of solution * density of solution * molar mass of HCl
Mass of NaOH solution = volume of solution * density of solution * molar mass of NaOH
For HCl:
volume of solution = 10.00 mL
density of solution = 1.00 g/mL (since it is given that it is a 1.00 M solution of HCl)
molar mass of HCl = 36.46 g/mol
Mass of HCl solution = 10.00 mL * 1.00 g/mL * 36.46 g/mol
For NaOH:
volume of solution = 115 mL
density of solution = 0.100 g/mL (since it is given that it is a 0.100 M solution of NaOH)
molar mass of NaOH = 39.997 g/mol
Mass of NaOH solution = 115 mL * 0.100 g/mL * 39.997 g/mol
Next, we can add the masses of the HCl and NaOH solutions together to get the mass of the solution:
Mass of solution = Mass of HCl solution + Mass of NaOH solution
After finding the mass of the solution, we can use the specific heat capacity of water (4.18 J/g°C) since the heat capacity of the calorimeter is given to be the same as that of 125 g of water.
Substituting the values into the equation for q:
q = mass of solution * s * ΔT
Calculating ΔT:
ΔT = final temperature - initial temperature
ΔT = 23.25 °C - 22.45 °C
Now we can calculate q.
To calculate the heat transfer (q) for this reaction, you can use the following formula:
q = m * c * ΔT
where
q = heat transfer (in Joules)
m = mass of the solution (in grams)
c = specific heat capacity (in J/g•°C)
ΔT = change in temperature (in °C)
We know that the heat capacity of the calorimeter is the same as that of 125 g of water, so we can use the specific heat capacity of water (4.184 J/g•°C) for our calculations.
First, let's calculate the mass of the solution. Since we are given the volume and concentration of the solutions, we can use the equation:
m1 * V1 = m2 * V2
where
m1 = molarity of HCl solution (in mol/L)
V1 = volume of HCl solution (in L)
m2 = molarity of NaOH solution (in mol/L)
V2 = volume of NaOH solution (in L)
Given:
m1 = 1.00 M (Molar)
V1 = 10.00 mL = 0.01000 L
m2 = 0.100 M (Molar)
V2 = 115 mL = 0.115 L
Using the equation, we get:
(1.00 M) * (0.01000 L) = (0.100 M) * (0.115 L)
0.010 mol = 0.0115 mol
The total moles of solute in the solution are 0.010 + 0.0115 = 0.0215 mol.
Next, let's calculate the mass of the solution. Since the density of water is 1 g/mL, the mass of the solution is equal to its volume (in mL) since the density is close to 1 g/mL:
Mass of solution = Volume of solution = 115 mL = 115 g
Now we can calculate the change in temperature (ΔT):
ΔT = Final temperature - Initial temperature
ΔT = 23.25 °C - 22.45 °C
ΔT = 0.80 °C
Finally, to calculate q, we can substitute the values into the formula:
q = m * c * ΔT
q = (115 g) * (4.184 J/g•°C) * (0.80 °C)
Calculating this expression will give you the value of q, which represents the heat transfer in joules for this reaction.
heat=2*125*Cw*(23.25-22.45)
Now that is the heat for .010*1mole of each reactant, or .020*1mole of NaCl (check this on balanced reaction).
so if you want to get heat per mole of NaCl, then divide heat above by .020