The combustion of 1.0 mol of sucrose liberates 5.65 x 10^3 KJ of heat. A calorimeter that has a heat capacity of 1.23 KJ/°C contains 0.60kg of water. How many grams of sucrose could be burned in the calorimeter to raise the temperature of the calorimeter and its content from 23°C to 27°C?
How many J are need to raise the T? That's
Total Q = q(water) + q(cal)
q(water) = mass H2O x specific heat H2O x (Tfinal-Tinitial)
q(water) = 600 g x 4.184J/g*C x (27-23) = abut 10,000 J but that's an estimate and you should do it and all the calculations that follow much more carefully.
q(cal) = 1,230 x dT = 1,230 x 4 = about 5,000 J
Q = about 15,000 J = 15 kJ.
You know 1 mol sucrose (that's 342 g sucrose) will liberate 5.65E3 kJ. So how many grams sucrose will it take? That's
342 g sucrose x (15 kJ/5.65E3 kJ) = ? g sucrose.
Remember all of these numbers are estimates.
To solve this problem, we need to calculate the amount of heat released by the combustion of sucrose and the amount of heat required to raise the temperature of the calorimeter and water content.
Given data:
- Heat released by 1.0 mol of sucrose = 5.65 x 10^3 KJ
- Heat capacity of the calorimeter = 1.23 KJ/°C
- Mass of water = 0.60 kg
- Initial temperature = 23°C
- Final temperature = 27°C
Step 1: Calculate the heat required to raise the temperature of the calorimeter and water content using the formula:
q = m * C * ΔT
where:
q = heat required
m = mass
C = specific heat capacity
ΔT = change in temperature
Given:
- m = mass of water = 0.60 kg
- C = specific heat capacity of the calorimeter = 1.23 KJ/°C
- ΔT = change in temperature = final temperature - initial temperature = 27°C - 23°C = 4°C
q = (0.60 kg) * (1.23 KJ/°C) * (4°C)
q = 2.95 KJ
Step 2: Calculate the number of moles of sucrose required to produce 2.95 KJ of heat.
Given:
- Heat released by 1.0 mol of sucrose = 5.65 x 10^3 KJ
Let x be the number of moles of sucrose.
(5.65 x 10^3 KJ / 1 mol) = (2.95 KJ / x)
Cross-multiplying and solving for x:
5.65 x 10^3 KJ * x = 2.95 KJ * 1 mol
x = (2.95 KJ * 1 mol) / (5.65 x 10^3 KJ)
x = 5.22 x 10^-4 mol
Step 3: Calculate the mass of sucrose required using the molar mass of sucrose.
Given:
- The molar mass of sucrose = 342.3 g/mol (approximately)
Mass of sucrose = x * molar mass
Mass of sucrose = (5.22 x 10^-4 mol) * (342.3 g/mol)
Mass of sucrose = 0.18 g (approximately)
Therefore, approximately 0.18 grams of sucrose could be burned in the calorimeter to raise the temperature from 23°C to 27°C.
To solve this problem, we need to determine the amount of heat energy required to raise the temperature of the calorimeter and its content, and then calculate the quantity of sucrose that would generate that much heat energy.
Let's break down the steps:
Step 1: Calculate the heat energy required to raise the temperature.
The heat energy required to raise the temperature of the calorimeter and the water can be calculated using the formula:
Q = mcΔT
where Q is the heat energy in joules, m is the mass of the water in kilograms, c is the specific heat capacity of water (4.18 J/g°C), and ΔT is the change in temperature.
First, we need to convert the mass of water from kilograms to grams:
0.60 kg * 1000 g/kg = 600 g
Next, we calculate the heat energy required:
Q = (600 g)(4.18 J/g°C)(27°C - 23°C)
Step 2: Convert the heat energy from joules to kilojoules.
Since the heat of combustion of sucrose is given in kilojoules, we need to convert the calculated heat energy from joules to kilojoules:
Q = Q / 1000
Step 3: Calculate the amount of sucrose that would generate the heat energy.
We know that 1.0 mol of sucrose liberates 5.65 x 10^3 kJ of heat. To find the amount of sucrose required for our calculated heat energy, we use the following equation:
mol = Q / heat of combustion
where mol is the number of moles of sucrose required.
Finally, we convert moles to grams by multiplying by the molar mass of sucrose.
Now we can proceed with the calculations:
Step 1:
Q = (600 g)(4.18 J/g°C)(27°C - 23°C)
Q = 600 g * 4.18 J/g°C * 4 °C
Q = 10,032 J
Step 2:
Q = 10,032 J / 1000 = 10.032 kJ
Step 3:
mol = 10.032 kJ / 5.65 x 10^3 kJ/mol = 0.001775 moles
Finally, we need to convert moles to grams:
mass = 0.001775 mol * 342 g/mol = 0.608 g
Therefore, approximately 0.608 grams of sucrose could be burned in the calorimeter to raise the temperature from 23°C to 27°C.