there's a 5.44 g sample of NH4NO3 and 150 g sample of water. So they ask for the change in enthalpy in kJ/mol. They give the temperature change from 16.2 degrees C to 18.6 degrees C. They also provide the specific heat capacity of the entire solution (155.4g) as 4.2 J/g*K. How do you solve for the change in enthalpy?? I kept getting the wrong answer. I thought you had to just use the equation q = mc*(change in temperature)
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To solve for the change in enthalpy (ΔH) in kJ/mol, you can follow these steps:
Step 1: Calculate the heat gained or lost by the water (qwater):
To calculate qwater, you can use the equation q = mcΔT, where:
- q is the heat gained or lost (in J)
- m is the mass of the water (in g)
- c is the specific heat capacity of the water (in J/g*K)
- ΔT is the change in temperature (in K)
Given:
- m (mass of water) = 150 g
- c (specific heat capacity of entire solution) = 4.2 J/g*K
- ΔT (change in temperature) = 18.6°C - 16.2°C = 2.4 K
Substitute the values into the equation:
qwater = (150 g) * (4.2 J/g*K) * (2.4 K)
Note: The mass of the water is used, as the specific heat capacity is given for the entire solution.
Step 2: Calculate the moles of NH4NO3:
To calculate the moles of NH4NO3, you can use the formula n = m/M, where:
- n is the number of moles
- m is the mass of NH4NO3 (in g)
- M is the molar mass of NH4NO3 (in g/mol)
Given:
- m (mass of NH4NO3) = 5.44 g
- M (molar mass of NH4NO3) = (1*14.01) + (4*1.008) + 14.01 + (3*16.00) = 80.05 g/mol
Substitute the values into the formula:
molesNH4NO3 = (5.44 g) / (80.05 g/mol)
Step 3: Calculate the change in enthalpy (ΔH):
To calculate ΔH, you can use the equation ΔH = q / n, where:
- ΔH is the change in enthalpy (in kJ/mol)
- q is the heat gained or lost (in J)
- n is the number of moles
Take the value of qwater calculated in Step 1 and divide it by the molesNH4NO3 calculated in Step 2 to get the change in enthalpy per mole.
ΔH = (qwater) / (molesNH4NO3)
Remember to convert the result to kJ/mol.
By following these steps, you should be able to calculate the change in enthalpy (ΔH) correctly. If you encounter any issues or have any further questions, feel free to ask!