Math

QuestionBurn 0.560 g0.560 \mathrm{~g} olive oil in a calorimeter with 370 g370 \mathrm{~g} water heating from 22.7C22.7{ }^{\circ} \mathrm{C} to 38.6C38.6^{\circ} \mathrm{C}. Find energy value in KJ/g\mathrm{KJ/g} to two significant figures.

Studdy Solution

STEP 1

Assumptions1. The mass of the olive oil sample is0.560 g. The mass of the water in the calorimeter is370 g3. The initial temperature of the water is 22.7C22.7{ }^{\circ} \mathrm{C}
4. The final temperature of the water is 38.6C38.6{ }^{\circ} \mathrm{C}
5. The specific heat capacity of water is 4.184J/gC4.184 \mathrm{J/g^{\circ}C}

STEP 2

First, we need to find the change in temperature of the water. We can do this by subtracting the initial temperature from the final temperature.
Δ=finalinitial\Delta =_{final} -_{initial}

STEP 3

Now, plug in the given values for the initial and final temperatures to calculate the change in temperature.
Δ=38.6C22.7C\Delta =38.6{ }^{\circ} \mathrm{C} -22.7{ }^{\circ} \mathrm{C}

STEP 4

Calculate the change in temperature.
Δ=38.6C22.7C=15.9C\Delta =38.6{ }^{\circ} \mathrm{C} -22.7{ }^{\circ} \mathrm{C} =15.9{ }^{\circ} \mathrm{C}

STEP 5

Next, we need to find the amount of energy absorbed by the water. We can do this by using the formula for heat absorbed or released, which is the product of the mass, specific heat capacity, and change in temperature.
q=m×c×Δq = m \times c \times \Delta

STEP 6

Plug in the values for the mass of the water, the specific heat capacity of water, and the change in temperature to calculate the heat absorbed.
q=370 g×4.184J/gC×15.9Cq =370 \mathrm{~g} \times4.184 \mathrm{J/g^{\circ}C} \times15.9{ }^{\circ} \mathrm{C}

STEP 7

Calculate the heat absorbed by the water.
q=370 g×4.184J/gC×15.9C=24600 Jq =370 \mathrm{~g} \times4.184 \mathrm{J/g^{\circ}C} \times15.9{ }^{\circ} \mathrm{C} =24600 \mathrm{~J}

STEP 8

Convert the energy from Joules to Kilojoules.
q=24.6 KJq =24.6 \mathrm{~KJ}

STEP 9

Finally, we need to find the energy value of the olive oil. We can do this by dividing the energy absorbed by the water by the mass of the olive oil sample.
Energyvalue=q/mEnergy\, value = q / m

STEP 10

Plug in the values for the heat absorbed and the mass of the olive oil to calculate the energy value.
Energyvalue=24.6 KJ/0.560 gEnergy\, value =24.6 \mathrm{~KJ} /0.560 \mathrm{~g}

STEP 11

Calculate the energy value of the olive oil.
Energyvalue=24.6 KJ/0.560 g=44 KJ/gEnergy\, value =24.6 \mathrm{~KJ} /0.560 \mathrm{~g} =44 \mathrm{~KJ/g}The energy value of the olive oil is44 KJ/g.

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