The reaction of hydrochloric acid and sodium hydroxide is exothermic
HCl +NaOH --> NaCl + H2O
In one experiment, a student placed 50.0 mL of 1.00 M HCl at 25.5 oC in a coffee cup calorimeter. To this was added 50.0 mL of 1.00 M NaOH solution, also at 25.5 oC. The mixture was stirred and the temperature rose to 37.8 oC. What is the heat of reaction in joules per mole of HCl? Assume the specific heat of the solutions is 4.184 J/g oC, densities are 1.00 g/mL, and no heat is lost to the cup or to the air.
mols HCl = M x L = 1.00 x 0.050 = 0.050
mols NaOH = M x L = 0.050
Total volume = 100 mL
qrxn = mass x specific heat x (Tfinal-Tinitial) = 100 g x 4.184 x (37.8-25.5) = ? J/0.050 mol HCl
So how much is q for 1 mol?
To calculate the heat of reaction in joules per mole of HCl, 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 specific heat, and ΔT is the change in temperature.
First, let's calculate the mass of the solution. Since both the HCl and NaOH solutions have the same volume of 50.0 mL and a density of 1.00 g/mL, the mass of each solution will be 50.0 g.
Next, we need to calculate the change in temperature, ΔT. ΔT is the final temperature minus the initial temperature. In this case, the initial temperature is 25.5°C and the final temperature is 37.8°C. Thus, ΔT is 37.8°C - 25.5°C = 12.3°C.
Now, we can calculate the heat released or absorbed, q. Since the reaction is exothermic, it releases heat. Therefore, q will be negative. We can use the equation:
q = -(mHCl * c * ΔT)
where mHCl is the mass of HCl.
We need to find the moles of HCl to convert to joules per mole of HCl. We can use the given concentration and volume of HCl.
mHCl = concentrationHCl * volumeHCl
where concentrationHCl is 1.00 M and volumeHCl is 50.0 mL.
Converting the volume of HCl from milliliters to liters, we have:
volumeHCl = 50.0 mL * (1 L / 1000 mL) = 0.0500 L
Now we can calculate the moles of HCl:
molesHCl = concentrationHCl * volumeHCl
Substituting the values, we get:
molesHCl = 1.00 M * 0.0500 L = 0.0500 mol HCl
Finally, we can calculate q:
q = -(0.0500 mol * 50.0 g/mol * 4.184 J/g°C * 12.3°C)
Calculating this expression will give you the heat released or absorbed in joules per mole of HCl.