How many grams of steam at 100 degrees celcuis would be required to raise the temperature of 35.8 g solid benzene (C6H6) from 5.5 - 45.0 degrees celcius.
(the melting point of benzene is 5.5 degrees celcius, delta H fusion for benzene is 9.87 kj/mol, specific heat for benzen is 1.63 J/gdegC and delta H vap. for steam at 100 degrees C is 40.7 kj/mol
q1 = heat to melt benzene.
q1 = mass benzene x heat fusion.
q2 = heat to move benzene from 5.5 to 45 C. Note the correct spelling of celsius.
q2 = mass benzene x specific heat benzene x (Tfinal-Tinitial).
q3 = heat lost by steam to condense to liquid water.
q3 = mass steam x heat vaporization. (This is the unknown).
q4 = heat lost by liquid water at 100 going to 45.
q4 = mass water x specific heat water x (Tfinal-Tinitial).
Total Q = q1 + q2 + q3 + q4.
Watch the signs and watch the units.
Adding heat is +. Heat lost is -.
How do i find the mass of water?
mass of water is the same as the mass of the steam (after it condenses). Just call mass steam X and mass water as X.
To solve this problem, we will need to calculate two separate quantities of heat: the heat required to melt the solid benzene and the heat required to raise its temperature from 5.5 to 45.0 degrees Celsius. We will then use these values to calculate the amount of steam needed to deliver the necessary heat.
Let's start by calculating the heat required to melt the benzene. The molar mass of benzene (C6H6) is approximately 78.11 g/mol.
1. Calculate the number of moles of solid benzene:
moles_benzene = mass_benzene / molar_mass_benzene
moles_benzene = 35.8 g / 78.11 g/mol
2. Calculate the heat required to melt the benzene:
q_fusion = moles_benzene * delta_H_fusion
q_fusion = moles_benzene * 9.87 kJ/mol
Next, we need to calculate the heat required to raise the temperature of the benzene from 5.5 to 45.0 degrees Celsius.
3. Calculate the temperature change:
delta_T = final_temperature - initial_temperature
delta_T = 45.0°C - 5.5°C
4. Calculate the heat required for the temperature change:
q_temp_change = mass_benzene * specific_heat * delta_T
q_temp_change = 35.8 g * 1.63 J/g°C * delta_T
Now, we can calculate the total heat required by adding the heat required for both the fusion and temperature change:
q_total = q_fusion + q_temp_change
Finally, using the given enthalpy change of vaporization for steam, we can calculate the mass of steam needed to deliver the total heat required.
5. Convert the total heat to kilojoules:
q_total_kJ = q_total / 1000
6. Calculate the number of moles of steam:
moles_steam = q_total_kJ / delta_H_vap
7. Calculate the mass of steam:
mass_steam = moles_steam * molar_mass_water
Therefore, to find the mass of steam required, the following steps are necessary:
1. Calculate the number of moles of solid benzene.
2. Calculate the heat required to melt the benzene.
3. Calculate the temperature change of solid benzene.
4. Calculate the heat required to raise the temperature of benzene.
5. Calculate the total heat required.
6. Convert the total heat to kilojoules.
7. Calculate the number of moles of steam.
8. Calculate the mass of steam using the molar mass of water.