Math / Numbers & Operations

Question $\angle p$ ts
Suppose there are 230.0 grams of water in a calorimeter, and the temperature increases from 52.1 degrees C to 57.2 degrees C . How much heat was released by the reaction that occurred in the calorimeter?
The heat capacity of water is $4.184 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}$ . You should record your answer in kJ as only a positive number, with the correct number of significant digits. For example, if you calculate that the amount of heat released was 8,413 J and that the answer should have 3 significant digits, you would enter " 8.41 " in the box below. $\square$

Studdy Solution

STEP 1

1. The mass of water in the calorimeter is $230.0$ grams.
2. The initial temperature of the water is $52.1$ degrees Celsius.
3. The final temperature of the water is $57.2$ degrees Celsius.
4. The specific heat capacity of water is $4.184 \, \mathrm{J/g^{\circ}C}$ .
5. We need to calculate the heat released in kilojoules (kJ) with the correct number of significant digits.

STEP 2

1. Calculate the change in temperature.
2. Use the formula for heat transfer to calculate the heat released.
3. Convert the heat from joules to kilojoules.
4. Determine the correct number of significant digits for the final answer.

STEP 3

Calculate the change in temperature ( $\Delta T$ ).
$\Delta T = T_{\text{final}} - T_{\text{initial}} = 57.2^\circ C - 52.1^\circ C$
$\Delta T = 5.1^\circ C$

STEP 4

Use the formula for heat transfer:
$q = m \cdot c \cdot \Delta T$
where $q$ is the heat absorbed or released, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature.
$q = 230.0 \, \mathrm{g} \times 4.184 \, \mathrm{J/g^{\circ}C} \times 5.1^\circ C$

STEP 5

Calculate the heat released in joules:
$q = 230.0 \times 4.184 \times 5.1 = 4911.672 \, \mathrm{J}$

STEP 6

Convert the heat from joules to kilojoules:
$q = \frac{4911.672 \, \mathrm{J}}{1000} = 4.911672 \, \mathrm{kJ}$

STEP 7

Determine the correct number of significant digits. The least number of significant digits in the given data is 3 (from the temperature change $5.1^\circ C$ ).
The final answer should have 3 significant digits:
$q = 4.91 \, \mathrm{kJ}$
The heat released by the reaction is:
$\boxed{4.91 \, \mathrm{kJ}}$

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Studdy Solution

STEP 1

STEP 2

1. Calculate the change in temperature.
2. Use the formula for heat transfer to calculate the heat released.
3. Convert the heat from joules to kilojoules.
4. Determine the correct number of significant digits for the final answer.

STEP 3

Calculate the change in temperature ( $\Delta T$ ).
$\Delta T = T_{\text{final}} - T_{\text{initial}} = 57.2^\circ C - 52.1^\circ C$
$\Delta T = 5.1^\circ C$

STEP 4

Use the formula for heat transfer:
$q = m \cdot c \cdot \Delta T$
where $q$ is the heat absorbed or released, $m$ is the mass, $c$ is the specific heat capacity, and $\Delta T$ is the change in temperature.
$q = 230.0 \, \mathrm{g} \times 4.184 \, \mathrm{J/g^{\circ}C} \times 5.1^\circ C$

STEP 5

Calculate the heat released in joules:
$q = 230.0 \times 4.184 \times 5.1 = 4911.672 \, \mathrm{J}$

STEP 6

Convert the heat from joules to kilojoules:
$q = \frac{4911.672 \, \mathrm{J}}{1000} = 4.911672 \, \mathrm{kJ}$

STEP 7

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Studdy Solution

STEP 1

STEP 2

1. Calculate the change in temperature.2. Use the formula for heat transfer to calculate the heat released.3. Convert the heat from joules to kilojoules.4. Determine the correct number of significant digits for the final answer.

STEP 3

Calculate the change in temperature (ΔT\Delta TΔT).ΔT=Tfinal−Tinitial=57.2∘C−52.1∘C\Delta T = T_{\text{final}} - T_{\text{initial}} = 57.2^\circ C - 52.1^\circ CΔT=Tfinal​−Tinitial​=57.2∘C−52.1∘CΔT=5.1∘C\Delta T = 5.1^\circ CΔT=5.1∘C

STEP 4

STEP 5

Calculate the heat released in joules:q=230.0×4.184×5.1=4911.672 Jq = 230.0 \times 4.184 \times 5.1 = 4911.672 \, \mathrm{J}q=230.0×4.184×5.1=4911.672J

STEP 6

Convert the heat from joules to kilojoules:q=4911.672 J1000=4.911672 kJq = \frac{4911.672 \, \mathrm{J}}{1000} = 4.911672 \, \mathrm{kJ}q=10004911.672J​=4.911672kJ

STEP 7

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1. Calculate the change in temperature.
2. Use the formula for heat transfer to calculate the heat released.
3. Convert the heat from joules to kilojoules.
4. Determine the correct number of significant digits for the final answer.

Calculate the change in temperature ( $\Delta T$ ).
$\Delta T = T_{\text{final}} - T_{\text{initial}} = 57.2^\circ C - 52.1^\circ C$
$\Delta T = 5.1^\circ C$

Calculate the heat released in joules:
$q = 230.0 \times 4.184 \times 5.1 = 4911.672 \, \mathrm{J}$

Convert the heat from joules to kilojoules:
$q = \frac{4911.672 \, \mathrm{J}}{1000} = 4.911672 \, \mathrm{kJ}$