Calorimetry Practice Problems

How much energy is needed to change the temperature of 50.0 g of water by 15.0°C?
How many grams of water can be heated from 20.0 C to 75°C using 12500.0 Joules?
What is the final temperature after 840 Joules is absorbed by 10.0g of water at 25.0°C?
The heat capacity of aluminum is 0.900 J/g’c.
How much energy is needed to raise the temperature of a 8.50 x 10g block of aluminum from 22.8? to 94.607?
A piece of metal weighing 59.047 g was heated to 100.0 °C and then put it into 100.0 mL of water (initially at 23.7 C). The metal and water were allowed to come to an equilibrium temperature, determined to be 27.8 °C. Assuming no heat lost to the environment, calculate the specific heat of the metal. (Hint: First calculate the heat absorbed by the water then use this value for “Q” to determine the specific heat of the metal in a second calculation)
In a coffee-cup calorimeter, 100.0 g of H:O and 100.0 mL of HCI are mixed. The HCI had an initial temperature of 44.6 C and the water was originally at 24.6 °C. After the reaction, the temperature of both substances is 31.3°C.
Was the reaction exothermic or endothermic? Explain.
Calculate how much heat the water lost or gained.

The Correct Answer and Explanation is:

1. How much energy is needed to change the temperature of 50.0 g of water by 15.0°C?

Use the formula:
q = mcΔT
Where:

m = 50.0 g
c = 4.18 J/g°C (specific heat of water)
ΔT = 15.0°C

q = (50.0)(4.18)(15.0) = 3135 J

✅ Answer: 3135 Joules

2. How many grams of water can be heated from 20.0°C to 75.0°C using 12500.0 Joules?

Rearrange q = mcΔT to solve for mass (m):

ΔT = 75.0 – 20.0 = 55.0°C
m = q / (cΔT) = 12500 / (4.18 × 55.0) ≈ 56.2 g

✅ Answer: 56.2 grams

3. What is the final temperature after 840 J is absorbed by 10.0g of water at 25.0°C?

Use q = mcΔT and solve for ΔT:
ΔT = q / (mc) = 840 / (10.0 × 4.18) ≈ 20.1°C
Final Temp = 25.0 + 20.1 = 45.1°C

✅ Answer: 45.1°C

4. How much energy is needed to raise the temperature of an 8.50 × 10 g block of aluminum from 22.8°C to 94.607°C?

First convert mass:
m = 8.50 × 10 = 85.0 g
c = 0.900 J/g°C
ΔT = 94.607 – 22.8 = 71.807°C
q = mcΔT = 85.0 × 0.900 × 71.807 ≈ 5489 J

✅ Answer: 5489 Joules

5. Specific heat of metal from calorimetry data

Knowns:

m_metal = 59.047 g
T_initial_metal = 100.0°C
T_final = 27.8°C
T_initial_water = 23.7°C
m_water = 100.0 g (100.0 mL of water = 100.0 g)
c_water = 4.18 J/g°C

First, calculate q_water:
ΔT_water = 27.8 – 23.7 = 4.1°C
q = mcΔT = 100.0 × 4.18 × 4.1 = 1713.8 J

Assume q_metal = -q_water = -1713.8 J
Now, solve for c_metal:
q = mcΔT ⇒ 1713.8 = 59.047 × c × (100.0 – 27.8) = 59.047 × c × 72.2
c = 1713.8 / (59.047 × 72.2) ≈ 0.401 J/g°C

✅ Answer: 0.401 J/g°C

6. Coffee-Cup Calorimeter Problem

Was the reaction exothermic or endothermic?
Initial temp of HCl = 44.6°C
Initial temp of water = 24.6°C
Final temp of both = 31.3°C

Water gained heat (24.6 → 31.3), HCl lost heat (44.6 → 31.3).
The system lost heat → exothermic.

✅ Answer: Exothermic

Calculate how much heat the water gained:

m = 100.0 g (water), c = 4.18 J/g°C, ΔT = 31.3 – 24.6 = 6.7°C
q = mcΔT = 100.0 × 4.18 × 6.7 ≈ 2800.6 J

✅ Answer: 2800.6 J

Explanation:

In a coffee-cup calorimeter, heat exchange occurs between the substances involved in a reaction without any heat loss to the surroundings, assuming ideal insulation. In this scenario, 100.0 g of water and 100.0 mL of HCl were mixed. The initial temperature of the HCl was 44.6°C, while the water was at 24.6°C. After the reaction, both substances reached a final temperature of 31.3°C.

The change in temperature indicates that heat flowed from the HCl (which cooled down) to the water (which warmed up). Since the HCl released heat and the water absorbed it, the reaction is exothermic—this means that energy was released into the surroundings during the reaction.

To calculate how much heat the water absorbed, we used the equation q = mcΔT. With a mass of 100.0 g, a specific heat capacity of 4.18 J/g°C, and a temperature change of 6.7°C (31.3°C – 24.6°C), the water gained approximately 2800.6 joules of energy. This amount of energy must have been lost by the HCl (assuming no heat was lost to the environment), which further supports the conclusion that the chemical reaction released heat.

Understanding whether a reaction is exothermic or endothermic is essential in calorimetry because it provides insight into the energy changes that occur during chemical processes. Exothermic reactions, such as neutralization reactions between acids and bases, often release energy as heat, making the surroundings warmer—an observation clearly supported by the data in this problem.