### Thermochemistry Problems:

Two Equations Needed

Problems using one part of the T-T graph

Problems using three parts of the T-T graph

Problems using four parts of the T-T graph

Problems using five parts of the T-T graph

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**Problem #1:** How many kJ are required to heat 45.0 g of H_{2}O at 25.0 °C and then boil it all away?

**Solution:**

Comment: We must do two calculations and then sum the answers.

1) The first calculation uses this equation:

q = (mass) (Δt) (C_{p})
This summarizes the information needed:

Δt = 75.0 °C

The mass = 45.0 g

C_{p} = 4.184 J g¯^{1} °C¯^{1}

2) Substituting, we have:

q = (45.0 g) (75.0 °C) (4.184 J g¯^{1} °C¯^{1})
q = 14121 J = 14.121 kJ

3) The second calculation uses this equation:

q = (moles of water) (ΔH_{vap})
This summarizes the information needed:

ΔH_{vap} = 40.7 kJ/mol

The mass = 45.0 g

The molar mass of H_{2}O = 18.0 gram/mol

4) Substituting, we obtain:

q = (45.0 g / 18.0 g mol¯^{1}) (40.7 kJ/mol)
q = 101.75 kJ

5) Adding:

101.75 kJ + 14.121 kJ = 116 kJ (to three sig figs)

**Problem #2:** How many kJ need to be removed from a 120.0 g sample of water, initially at 25.0 °C, in order to freeze it at 0 °C? (Area three, then area two on the time-temperature graph.)

**Solution:**

1) The first calculation:

q = (mass) (Δt) (C_{p})
q = (120.0 g) (25.0 °C) (4.184 J g¯^{1} °C¯^{1})

q = 12,552 J = 12.552 kJ

2) The second calculation:

q = (moles of water) (ΔH_{vap})
q = (120.0 g / 18.0 g mol¯^{1}) (6.02 kJ/mol)

q = 40.13 kJ

3) Summing up the values from the two steps gives 52.8 kJ.

**Problem #3:** You are given 12.0 g of ice at -5.00 °C. How much energy is needed to melt the ice completely to water?

**Solution:**

1) The first calculation:

q = (mass) (Δt) (C_{p})
q = (12.0 g) (5.0 °C) (2.06 J g¯^{1} °C¯^{1})

q = 123.6 J = 0.1236 kJ

2) The second calculation:

q = (moles of water) (ΔH_{vap})
q = (12.0 g / 18.0 g mol¯^{1}) (6.02 kJ/mol)

q = 4.0133 kJ

3) Summing up the values from the two steps gives 4.14 kJ, to three significant figures.

Problems using one part of the T-T graph

Problems using three parts of the T-T graph

Problems using four parts of the T-T graph

Problems using five parts of the T-T graph

Go to the Time-Temperature Graph file

Return to Thermochemistry Menu