A quantity of 85.0 mL of 0.900 M HCl is mixed with 85.0 mL of 0.900 M KOH in a constant-pressure calorimeter that has a heat capacity of 325 J/C. If the initial temperatures of both solutions are the same at 18.24C, what is the final temperature of the mixed solution? The heat of neutralisation is -56.2 kJ/mol. Assume the density and specific heat of the solutions to be the same as those of water.
To solve this problem, we can use the heat transfer equation:
q = mcΔT
where:
q = heat transferred (in Joules)
m = mass of the solution (in grams)
c = specific heat capacity of the solution (in J/g·°C)
ΔT = change in temperature (in °C)
First, let's calculate the initial heat transfer for both the HCl and KOH solutions separately.
For HCl solution:
mHCl = VHCl × DHCl
= (85.0 mL × 1.00 g/mL) × (0.900 mol/L × 36.4611 g/mol)
For KOH solution:
mKOH = VKOH × DKOH
= (85.0 mL × 1.00 g/mL) × (0.900 mol/L × 56.1056 g/mol)
Next, let's calculate the heat generated by the reaction:
qreaction = n × ΔHneutralization
Here, n is the number of moles of HCl and KOH, and ΔHneutralization is the heat of neutralization.
n = (0.900 mol/L) × (0.0850 L)
Now we can calculate ΔT:
qreaction = qHCl + qKOH = (mHCl × c × ΔTHCl) + (mKOH × c × ΔTKOH)
Thus,
qreaction = n × ΔHneutralization
= (mHCl × c × ΔTHCl) + (mKOH × c × ΔTKOH)
Rearranging and solving for ΔT:
ΔT = qreaction / (mHCl × c + mKOH × c)
Finally, we can calculate the final temperature using:
Tfinal = Tinitial + ΔT
Let's plug in the given values and calculate the final temperature.
To find the final temperature of the mixed solution, we can use the heat transfer equation:
q = mcdeltaT
Where:
q = heat transferred
m = mass of the solution
c = specific heat capacity of the solution
deltaT = change in temperature
First, let's calculate the heat transferred using the heat of neutralization and the moles of HCl and KOH reacted.
1. Calculate the moles of HCl:
Moles of HCl = volume (L) × molarity
Moles of HCl = 0.085 L × 0.900 mol/L
2. Calculate the moles of KOH:
Moles of KOH = volume (L) × molarity
Moles of KOH = 0.085 L × 0.900 mol/L
3. Determine the limiting reactant:
The balanced equation for the neutralization reaction between HCl and KOH is:
HCl + KOH → H2O + KCl
From the balanced equation, we can see that one mole of HCl reacts with one mole of KOH. Therefore, the limiting reactant will be the one with fewer moles. In this case, both HCl and KOH have the same number of moles, so HCl is the limiting reactant.
4. Calculate the heat transferred using the heat of neutralization:
Heat transferred = moles of HCl × heat of neutralization
Heat transferred = 0.085 mol × (-56.2 kJ/mol)
5. Convert heat transferred to joules:
Heat transferred = -56.2 kJ × 1000 J/kJ = -56,200 J
Next, we need to calculate the total mass of the solution by adding the masses of HCl and KOH:
Mass of HCl = volume × density × specific heat of water
Mass of HCl = 0.085 L × 1.00 g/mL × 4.18 J/g•°C
Mass of KOH = volume × density × specific heat of water
Mass of KOH = 0.085 L × 1.00 g/mL × 4.18 J/g•°C
Total mass of the solution = mass of HCl + mass of KOH
Now, let's substitute the values into the heat transfer equation:
q = (mass of the solution) × (specific heat capacity) × (change in temperature)
Rearrange the equation to solve for deltaT:
deltaT = q / (mass of the solution × specific heat capacity)
Substitute the calculated values:
deltaT = -56,200 J / ((mass of the solution) × 325 J/°C)
Finally, to find the final temperature, add deltaT to the initial temperature:
Final temperature = initial temperature + deltaT
Now, you can calculate the final temperature using the given values and the steps explained above.
q = mc*dT
56200 = 170 x 4.18 x (T-18.24)