1) A 15.0 g sample of nickel metal is heated to 100.0 C and dropped into 55.0 g of water, initially at 23.0 C. Calculate the final temperature of the nickel and the water, if the specific heat capacity of nickel is 0.444 j / g x C.
2) In a coffee-cup calorimeter, 1.60 g of NH4NO3 is mixed with 75.0 g of water at an initial temperature of 25.00°C. After dissolution of the salt, the final temperature of the calorimeter contents is 23.34°C. Assuming the solution has a heat capacity of 4.18 J/°C·g and assuming no heat loss to the calorimeter, calculate the enthalpy change for the dissolution of NH4NO3 in units of kJ/mol.
1.
[mass H2O x specific heat water x (Tfinal-
Tinitial)] + [mass nickel x specific heat nickel x (Tfinal-Tinitial)] = 0
Solve for Tfinal.
2.
How much heat was exchanged when the NH4NO3 went into solution.
q = mass H2O x specific heat water x (Tfinal-Tinitial) = ??
?? will be J/1.60 g NH4NO3.
Convert that to per mole NH4NO3 and convert that to kJ. The final answer will be kJ/mol.
1) To calculate the final temperature of the nickel and water mixture, we can use the principle of conservation of energy and the equation:
q_ni = q_water
where q_ni is the heat absorbed by the nickel and q_water is the heat released by the water.
The heat absorbed by the nickel can be calculated using the equation:
q_ni = m_ni * c_ni * ΔT_ni
where m_ni is the mass of nickel, c_ni is the specific heat capacity of nickel, and ΔT_ni is the change in temperature of the nickel.
The heat released by the water can be calculated using the equation:
q_water = m_water * c_water * ΔT_water
where m_water is the mass of water, c_water is the specific heat capacity of water, and ΔT_water is the change in temperature of the water.
Given:
m_ni = 15.0 g
c_ni = 0.444 J/g°C
m_water = 55.0 g
c_water = 4.18 J/g°C
ΔT_ni = T_final - T_initial_ni (T_initial_ni = 100.0°C)
ΔT_water = T_final - T_initial_water (T_initial_water = 23.0°C)
Since the system reaches equilibrium, T_final for both the nickel and water will be the same. Therefore, ΔT_ni = ΔT_water = ΔT.
Substituting the given values into the equations, we have:
q_ni = 15.0 g * 0.444 J/g°C * (T_final - 100.0°C)
q_water = 55.0 g * 4.18 J/g°C * (T_final - 23.0°C)
Since q_ni = q_water, we can set the two equations equal to each other and solve for T_final:
15.0 g * 0.444 J/g°C * (T_final - 100.0°C) = 55.0 g * 4.18 J/g°C * (T_final - 23.0°C)
Simplifying the equation:
6.66 J/°C * (T_final - 100.0°C) = 229.9 J/°C * (T_final - 23.0°C)
6.66 * T_final - 666 J = 229.9 * T_final - 5294.7 J
6.66 * T_final - 229.9 * T_final = 666 J - 5294.7 J
-223.24 * T_final = -4628.7 J
T_final = -4628.7 J / -223.24 = 20.7°C
Therefore, the final temperature of the nickel and water mixture is approximately 20.7°C.
2) To calculate the enthalpy change for the dissolution of NH4NO3 in kJ/mol, we can use the equation:
ΔH = q / n
where ΔH is the enthalpy change, q is the heat absorbed or released during the reaction, and n is the number of moles of NH4NO3.
The heat absorbed or released during the reaction can be calculated using the equation:
q = m_solution * c_solution * ΔT_solution
where m_solution is the mass of the solution, c_solution is the specific heat capacity of the solution, and ΔT_solution is the change in temperature of the solution.
Given:
m_solution = 1.60 g NH4NO3 + 75.0 g water = 76.6 g
c_solution = 4.18 J/°C·g
ΔT_solution = T_final - T_initial (T_initial = 25.00°C, T_final = 23.34°C)
To calculate the number of moles of NH4NO3, we can use the equation:
n = mass / molar mass
where mass is the mass of NH4NO3 and molar mass is the molar mass of NH4NO3.
Given:
mass = 1.60 g
molar mass of NH4NO3 = 80.04 g/mol
Substituting the given values into the equations, we have:
n = 1.60 g / 80.04 g/mol = 0.02 mol
q = 76.6 g * 4.18 J/°C·g * (23.34°C - 25.00°C)
Simplifying the equation:
q = -157.375 J
ΔH = -157.375 J / 0.02 mol = -7868.75 J/mol
Since the answer is required in kJ/mol, we divide by 1000 to convert J to kJ:
ΔH = -7.86875 kJ/mol
Therefore, the enthalpy change for the dissolution of NH4NO3 is approximately -7.87 kJ/mol.
To solve both questions, we will use the equation:
q = m * c * ΔT
where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.
Let's start with question 1:
1) To find the final temperature, we need to calculate the heat transferred between the nickel and water.
First, let's find the heat transferred between the nickel and water:
q_ni = m_ni * c_ni * ΔT_ni
Here, m_ni is the mass of the nickel (15.0 g), c_ni is the specific heat capacity of nickel (0.444 J/g°C), and ΔT_ni is the change in temperature.
Next, let's find the heat transferred between the water and nickel:
q_wa = m_wa * c_wa * ΔT_wa
Here, m_wa is the mass of the water (55.0 g), c_wa is the specific heat capacity of water (4.18 J/g°C), and ΔT_wa is the change in temperature.
Since heat lost by the nickel is gained by the water, we can equate the two equations:
q_ni = -q_wa
m_ni * c_ni * ΔT_ni = -m_wa * c_wa * ΔT_wa
Substituting the given values:
15.0 g * 0.444 J/g°C * ΔT_ni = -55.0 g * 4.18 J/g°C * ΔT_wa
Now, let's solve for the change in temperature of the nickel (ΔT_ni):
ΔT_ni = (-55.0 g * 4.18 J/g°C * ΔT_wa) / (15.0 g * 0.444 J/g°C)
Now calculate the final temperature of the system by adding the change in temperature to the initial temperature of the water:
T_final = 23.0°C + ΔT_wa
2) To calculate the enthalpy change for the dissolution of NH4NO3, we will use the equation:
ΔH = q_solution / n
where ΔH is the enthalpy change, q_solution is the heat transferred to the solution, and n is the number of moles of NH4NO3.
First, let's calculate the heat transferred to the solution (q_solution):
q_solution = -(q_calorimeter + q_water)
Here, q_calorimeter is the heat absorbed by the calorimeter, and q_water is the heat absorbed by the water.
The heat absorbed by the calorimeter (q_calorimeter) can be calculated using the equation:
q_calorimeter = m_calorimeter * c_calorimeter * ΔT_calorimeter
Here, m_calorimeter is the mass of the calorimeter, c_calorimeter is the specific heat capacity of the calorimeter, and ΔT_calorimeter is the change in temperature.
Substituting the given values:
q_calorimeter = 75.0 g * 4.18 J/°C·g * (23.34°C - 25.00°C)
Now, let's calculate the heat absorbed by the water (q_water) using the equation:
q_water = m_water * c_water * ΔT_water
Here, m_water is the mass of the water, c_water is the specific heat capacity of the water, and ΔT_water is the change in temperature.
Substituting the given values:
q_water = 75.0 g * 4.18 J/°C·g * (23.34°C - 25.00°C)
Finally, substitute the values of q_calorimeter and q_water into the equation for q_solution:
q_solution = -(q_calorimeter + q_water)
Now, to calculate the enthalpy change:
ΔH = q_solution / n
Here, n is the number of moles of NH4NO3. To find n, we use the molar mass of NH4NO3 and the given mass (1.60 g):
n = mass / molar mass
Calculate the molar mass of NH4NO3 using the atomic masses:
NH4NO3 = 14.01 g/mol (N) + 4 * 1.01 g/mol (H) + 3 * 16.00 g/mol (O)
Once we have n, substitute the values into the equation for ΔH to get the enthalpy change in units of kJ/mol.
That's it! You should now have the final temperature for question 1 and the enthalpy change for question 2.