SME
General Chemistry I
Thermochemistry
Use this for “50 mL of 1.00 M HCl and 50 mL of 1.00 M NaOH are mixed in a coffee-cup calorimeter. The temperature rises from 22.00 °C to 28.70 °C. Find ΔH per mole of water formed.”
Diagram
Heat taken in by the water: q = mcΔT = 100 × 4.184 × 6.7 = 2,803 J
The water warmed: the reaction gave off 2,803 J.
Exothermic.
This is an example. Type your own values to start a new problem.
q (J)
=
m (g)
×
c (J/(g·°C))
×
ΔT (°C)
ΔH (kJ/mol)
=
−
q (J)
÷
n (mol)
T₁
Starting temperature
example · °C
T₂
Final temperature
example · °C
Formulas
ΔT
=
T₂
−
T₁
6.7 = 28.7 − 22
q
=
m
×
c
×
ΔT
2,803 = 100 × 4.184 × 6.7
ΔH
=
−
q
1,000 ×
n
−56.07
=
−
2,803
1,000 × 0.05
Assumptions
•
The solution has water’s density (1.00 g/mL) and specific heat (4.184 J/(g·°C)), so 100 mL of it weighs 100 g.
•
No heat goes into the cup or the air: the solution takes in all the heat the reaction gives off.
•
The reaction’s heat is −q, so a temperature rise means ΔH < 0 (exothermic). ΔH is per mole of the reaction as written, here per mole of water formed.
Step-by-step
WE KNOW
m = 100 g, c = 4.184 J/(g·°C), T₁ = 22 °C, T₂ = 28.7 °C, n = 0.05 mol
FIND
change in temperature (ΔT), heat the solution takes in (q), enthalpy change per mole (ΔH)
Step 1 · Find change in temperature (ΔT)
Use ΔT = T₂ − T₁
The change is the final temperature less the starting one: a rise is positive.
ΔT = 28.7 − 22
ΔT = 6.7 °C
Step 2 · Find heat the solution takes in (q)
Use q = m × c × ΔT
The solution’s heat: its mass times its specific heat times how much it warmed.
q
=
100
×
4.184
×
6.7
q
=
418.4
×
6.7
q
=
2,803
J
Step 3 · Find enthalpy change per mole (ΔH)
Use ΔH = −q ÷ (1,000 × n)
The
reaction
gave
off
what
the
solution
took
in,
so
its
heat
is
−
q
.
Share
it
among
the
moles;
÷
1000
turns
J
into
kJ.
ΔH
=
−
2,803.28
1,000 × 0.05
ΔH
=
−
2,803.28
50
ΔH = −56.07 kJ/mol
Check
Put the numbers back in. Both sides should match.
6.7 = 28.7 − 22 ✓
2,803 = 100 × 4.184 × 6.7 ✓
−56.07
=
−
2,803.28
1,000 × 0.05
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
More problem types
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