Problem 117 - Chemistry Matter and Change

Question

When 5.00 g of a compound was burned in a calorimeter, the temperature of 2.00 \(\mathrm{kg}\) of water increased from \(24.5^{\circ} \mathrm{C}\) to \(40.5^{\circ} \mathrm{C}\) . How much heat would be released by the combustion of 1.00 \(\mathrm{mol}\) of the compound (molar mass \(=46.1 \mathrm{g} / \mathrm{mol} ) ?(\text {Chapter } 15)\)

Step-by-Step Solution

Answer

The heat released by the combustion of 1.00 mol of the compound is calculated using the following steps: 1. Calculate the heat absorbed by water: q_water = (2000 g) * (4.18 J/g°C) * (40.5°C - 24.5°C) 2. The heat released by the combustion equals the heat absorbed by water: q_combustion = q_water 3. Find the moles of the compound burned: n_compound = 5.00g / 46.1g/mol 4. Calculate the heat released per mole of combustion: q_combustion_per_mole = ( (2000 g) * (4.18 J/g°C) * (40.5°C - 24.5°C) ) / (5.00g / 46.1g/mol) Thus, the heat released by the combustion of 1.00 mol of the compound is q_combustion_per_mole.

Step 1: Calculate the heat absorbed by water.

We can calculate the heat absorbed by water, q_water, using the following formula: q_water = m_water * c_water * ΔT_water where m_water = mass of water = 2.00 kg = 2000 g (We need to convert kilograms to grams) c_water = specific heat capacity of water = 4.18 J/g°C ΔT_water = change in temperature of water = T_final - T_initial = 40.5°C - 24.5°C Now, let's calculate the heat absorbed by water: q_water = (2000 g) * (4.18 J/g°C) * (40.5°C - 24.5°C)

Step 2: Calculate the heat released by the combustion of the compound.

As the energy absorbed by water equals the energy released by the compound through the combustion process, we can write: q_combustion = q_water Calculate q_combustion: q_combustion = (2000 g) * (4.18 J/g°C) * (40.5°C - 24.5°C)

Step 3: Find the moles of the compound burned.

We can find the moles of the compound burned, n_compound, using the following formula: n_compound = mass_compound / molar_mass where mass_compound = 5.00 g molar_mass = 46.1 g/mol Calculate the moles of the compound burned: n_compound = 5.00g / 46.1g/mol

Step 4: Find the heat released per mole of combustion.

We can find the heat released per mole of combustion, q_combustion_per_mole, using the following formula: q_combustion_per_mole = q_combustion / n_compound Now substitute the value of q_combustion and n_compound that we calculated earlier: q_combustion_per_mole = ( (2000 g) * (4.18 J/g°C) * (40.5°C - 24.5°C) ) / (5.00g / 46.1g/mol) Now, we have the heat released by the combustion of 1.00 mol of the compound.

Key Concepts

Calorimetry

Calorimetry is a branch of thermochemistry that deals with measuring the amount of heat released or absorbed during chemical reactions. When a substance undergoes combustion, it releases heat that can be measured using a calorimeter. A calorimeter is an insulated device that helps track the heat exchanged with the surroundings, ensuring accuracy in measuring the energy change. In an experiment, such as burning a compound to warm water, the calorimeter captures and quantifies the heat transferred.

• This process involves carefully measuring the temperature change in the substance causing the reaction.
• The heat measured by the calorimeter reflects the energy change of the system, allowing precise calculations of heat transfer.

This process is especially important in finding how much energy is involved in the combustion of substances, helping ensure that experiments yield consistent results when determining energy transfer in chemical reactions.

Heat Transfer

Heat transfer is the movement of thermal energy from a hotter object to a cooler one. In calorimetry experiments, the heat from the burning compound is transferred to the water in the calorimeter. This causes an increase in the water's temperature, which can then be measured.

• The direction of heat transfer follows from the substance releasing heat (the burning compound) to the substance absorbing it (the water).
• The temperature change of the water is directly related to the amount of heat transferred.

Heat transfer continues until thermal equilibrium is established, meaning that the substance releasing heat and the substance absorbing heat reach the same temperature. Understanding heat transfer is crucial for accurately determining energy changes in reactions.

Specific Heat Capacity

Specific heat capacity is a property of a substance that measures how much heat is required to change its temperature by one degree Celsius (or Kelvin). Water, for example, has a specific heat capacity of 4.18 J/g°C, which signifies it takes 4.18 joules of energy to raise the temperature of one gram of water by one degree Celsius.

• The specific heat capacity is essential for calculating the amount of heat absorbed or released by a substance during a temperature change.
• It helps determine the efficiency of a substance to store or release heat compared to others. For instance, water has a high specific heat capacity, meaning it can absorb a lot of heat before its temperature changes significantly.

In the calorimetry experiment, the specific heat capacity of water is critical for calculating the heat absorbed due to the controlled combustion of the compound. It aids in quantifying the total heat change during the reaction, enabling precise adjustments and predictions in thermochemical processes.