A sample of carbon,3.0g, was burned to carbon dioxide in a copper calorimeter.The mass of the calorimeter was 1.5kg and the mass of water in the calorimeter was 2kg.The initial temperature was 20°c and the final temperature was 31°c.Calculate the heat liberated for the combustion of 1g of carbon. The specific heat capacity of carbon and water are 0.389 and 4.18
I'm at a loss with this problem. Two interpretations:
a. 3.0 g C completely burned. If so then specific heat C isn't needed (since no C is left over). Calculate heat then divide by 3 to find for 1 g.
b. Only 1.0 g of the 3.0 g sample is burned in which case th4e other 2.0 g absorbs some of the heat so heat is absorbed by the calorimeter, the water, and the other 2.0 g C.
Well, let's calculate the heat liberated for the combustion of 1g of carbon.
First, we need to find the heat absorbed by the water. The specific heat capacity of water is 4.18 J/g°C. The change in temperature is 31°C - 20°C = 11°C.
So, the heat absorbed by the water = mass of water * specific heat capacity of water * change in temperature
= 2g * 4.18 J/g°C * 11°C
≈ 91.96 J
Next, we need to find the heat absorbed by the copper calorimeter. The specific heat capacity of copper is not given, but we'll assume it to be fairly small compared to water.
So, the heat absorbed by the copper calorimeter ≈ 0.
Now, let's find the total heat liberated in the combustion of 3.0g of carbon, which is equivalent to the heat absorbed by the water and copper calorimeter.
Total heat liberated = Heat absorbed by the water + Heat absorbed by the copper calorimeter
= 91.96 J + 0 J
≈ 91.96 J
Finally, let's calculate the heat liberated for the combustion of 1g of carbon.
Heat liberated for 1g of carbon = Total heat liberated / mass of carbon
= 91.96 J / 3.0g
≈ 30.65 J/g
So, the heat liberated for the combustion of 1g of carbon is approximately 30.65 J/g.
To calculate the heat liberated for the combustion of 1g of carbon, we need to calculate the heat gained by the water and the calorimeter.
1. Calculate the heat gained by the water:
Heat gained by water = mass of water × specific heat capacity of water × change in temperature
= 2kg × 4.18 J/g°C × (31°C - 20°C)
= 2kg × 4.18 J/g°C × 11°C
= 91.82 J
2. Calculate the heat gained by the calorimeter:
Heat gained by calorimeter = mass of calorimeter × specific heat capacity of calorimeter × change in temperature
= 1.5kg × 0.389 J/g°C × (31°C - 20°C)
= 1.5kg × 0.389 J/g°C × 11°C
= 6.438 J
3. Calculate the total heat liberated for the combustion of 3.0g of carbon:
Total heat liberated = heat gained by water + heat gained by calorimeter
= 91.82 J + 6.438 J
= 98.258 J
4. Calculate the heat liberated for the combustion of 1g of carbon:
Heat liberated for 1g of carbon = Total heat liberated / mass of carbon
= 98.258 J / 3.0g
= 32.75 J/g
Therefore, the heat liberated for the combustion of 1g of carbon is 32.75 J/g.
To calculate the heat liberated for the combustion of 1g of carbon, we need to determine the amount of heat transferred from the combustion process to the water in the calorimeter.
1. Calculate the heat absorbed by the water:
- The specific heat capacity of water (c) is given as 4.18 J/g°C.
- The mass of water (m) is given as 2kg, which is equal to 2000g.
- The change in temperature (ΔT) is the final temperature (31°C) minus the initial temperature (20°C), which is 11°C.
The heat absorbed by the water (Q1) can be calculated using the formula:
Q1 = m * c * ΔT
= 2000g * 4.18 J/g°C * 11°C
= 92280 J
2. Calculate the heat absorbed by the calorimeter:
- The mass of the calorimeter (m_calorimeter) is given as 1.5kg, which is equal to 1500g.
- The specific heat capacity of copper (c_calorimeter) is not provided, but we can assume it to be similar to water (4.18 J/g°C) since both are metals.
The heat absorbed by the calorimeter (Q2) can be calculated using the same formula:
Q2 = m_calorimeter * c_calorimeter * ΔT
= 1500g * 4.18 J/g°C * 11°C
= 81990 J
3. Calculate the total heat liberated during the combustion process:
- The total heat liberated is the sum of the heat absorbed by the water and the calorimeter.
- The heat liberated during the combustion process (Q_total) can be calculated as:
Q_total = Q1 + Q2
= 92280 J + 81990 J
= 174270 J
4. Calculate the heat liberated for the combustion of 1g of carbon:
- Given that the mass of the carbon sample is 3.0g, we can calculate the heat liberated for 1g of carbon (Q_per_gram):
Q_per_gram = Q_total / mass_of_carbon_sample
= 174270 J / 3.0g
= 58090 J/g
Therefore, the heat liberated for the combustion of 1g of carbon is approximately 58090 J.