Calculate the number of joules required to melt 57.4g of benzene at 5.5 degrees celsius?
The heat of fusion for benzene is 9.87 KJ/mol and specific heat for liquid benzene is 1.63 J/g*deg)
q = mass benzene x heat fusion. Watch the units.
Well, if we want to calculate the number of joules required to melt a certain amount of benzene, we need to consider two things: the heat of fusion and the change in temperature.
First, let's calculate the heat required to melt the benzene. The heat of fusion is given as 9.87 kJ/mol, so we need to convert grams to moles. The molar mass of benzene is approximately 78.11 g/mol.
So, 57.4 g of benzene is equal to approximately 0.735 moles (57.4 g / 78.11 g/mol).
Now let's calculate the energy required to melt the benzene:
Energy required = heat of fusion * moles
Energy required = 9.87 kJ/mol * 0.735 mol
Multiplying these values gives us 7.24745 kJ (rounded to five decimal places).
Now, we need to take into account the change in temperature. The specific heat for liquid benzene is given as 1.63 J/g*°C. We have 57.4g of benzene and a temperature change of 5.5°C.
The energy required for the temperature change can be calculated as follows:
Energy required = mass * specific heat * temperature change
Energy required = 57.4 g * 1.63 J/g*°C * 5.5°C
Multiplying these values gives us 529.453 J (rounded to three decimal places).
Now, to find the total energy required, we simply add the energy required for melting to the energy required for the temperature change:
Total energy required = energy required for melting + energy required for temperature change
Total energy required = 7.24745 kJ + 529.453 J
Adding these values gives approximately 7.77690345 kJ (rounded to eight decimal places) or 7776.90345 J in scientific notation.
So, humor aside, the number of joules required to melt 57.4g of benzene at 5.5 degrees Celsius is approximately 7776.90345 J.
To calculate the number of joules required to melt a given amount of benzene, we need to consider two factors: the heat of fusion and the change in temperature.
Step 1: Calculate the moles of benzene:
First, we need to convert the mass of benzene to moles. The molar mass of benzene (C6H6) is 78.11 g/mol.
Number of moles = mass / molar mass
Number of moles = 57.4 g / 78.11 g/mol
Step 2: Calculate the heat required for fusion:
The heat of fusion for benzene is given as 9.87 kJ/mol.
Heat required for fusion = moles of benzene * heat of fusion
Heat required for fusion = (57.4 g / 78.11 g/mol) * 9.87 kJ/mol
Step 3: Calculate the change in temperature:
The change in temperature is given as 5.5 degrees Celsius. Since benzene is at its melting point, no temperature change is occurring during the fusion process.
Change in temperature = 5.5 degrees Celsius
Step 4: Calculate the total amount of energy required:
To calculate the total amount of energy required, we need to consider the heat required for fusion and any additional heat required to raise the temperature to the final temperature.
Total energy required = heat required for fusion + heat required for temperature change
Since the temperature is constant during fusion, the heat required for temperature change is zero.
Total energy required = heat required for fusion
Therefore, the number of joules required to melt 57.4g of benzene at 5.5 degrees Celsius is equal to the heat required for fusion, which can be calculated as follows:
Total energy required = (57.4 g / 78.11 g/mol) * 9.87 kJ/mol
To calculate the number of joules required to melt a specific amount of benzene, we need to consider two aspects: the heat energy required to raise the temperature of the benzene to its melting point and the heat energy required to melt the benzene.
First, we calculate the heat energy required to raise the temperature of benzene to its melting point:
Q1 = mass × specific heat × change in temperature
= 57.4g × 1.63 J/g*°C × (5.5°C - 0°C)
= 57.4g × 1.63 J/g*°C × 5.5°C
Next, we calculate the heat energy required to melt the benzene:
Q2 = mass × heat of fusion
= 57.4g × (9.87 KJ/mol ÷ 1000 J/KJ)
= 57.4g × 9.87 J/g
Finally, we add the two quantities together to obtain the total heat energy required:
Total heat energy (Q) = Q1 + Q2
Therefore, to calculate the number of joules required to melt 57.4g of benzene at 5.5°C, you would calculate:
Total heat energy (Q) = (57.4g × 1.63 J/g*°C × 5.5°C) + (57.4g × 9.87 J/g)
After performing the calculations, you will have the number of joules required to melt the given amount of benzene at the given temperature.