When 1.0 g of ammonium nitrate, NH4NO3, dissolves in 50.0 g of water, the temperature of the water drops from 25.0C to 23.32C. What is the molar heat (H) of solution in kJ/mol?
To calculate the molar heat of solution, we can use the equation:
H = q / n
Where:
H is the molar heat of solution (in kJ/mol),
q is the heat transferred (in kJ),
and n is the number of moles of solute.
First, let's calculate the heat transferred (q).
The heat transferred can be calculated using the equation:
q = m * c * ΔT
Where:
q is the heat transferred (in kJ),
m is the mass of the solvent (in g),
c is the specific heat capacity of water (4.18 J/g°C),
ΔT is the change in temperature (in °C).
Given:
Mass of water (solvent), m = 50.0 g
Initial temperature, T1 = 25.0°C
Final temperature, T2 = 23.32°C
ΔT = T2 - T1 = 23.32°C - 25.0°C = -1.68°C
q = 50.0 g * 4.18 J/g°C * (-1.68°C)
Convert grams to kilograms:
q = 0.050 kg * 4.18 J/g°C * (-1.68°C)
Now we have q in Joules. To convert it to kilojoules:
q = 0.050 kg * 4.18 J/g°C * (-1.68°C) /1000 = -0.0013902 kJ
Next, let's calculate the number of moles of NH4NO3.
Given:
Mass of ammonium nitrate, m = 1.0 g
Molar mass of ammonium nitrate, MM = (1 * 14) + (4 * 1) + (1 * 14) + (3 * 16) = 80 g/mol
n (in moles) = m / MM
n = 1.0 g / 80 g/mol
Now, let's calculate H.
H = q / n
H = -0.0013902 kJ / (1.0 g / 80 g/mol)
H = -0.0013902 kJ * (80 g/mol / 1.0 g)
H = -0.111216 kJ/mol
Therefore, the molar heat (H) of solution of ammonium nitrate is approximately -0.111 kJ/mol.
To find the molar heat of solution in kJ/mol, you can use the formula:
H = q / n
where H is the molar heat of solution, q is the heat absorbed or released during the process, and n is the number of moles of the solute.
To calculate q, we need to use the equation:
q = m × c × ΔT
where m is the mass of the water, c is the specific heat capacity of water, and ΔT is the change in temperature.
Given data:
Mass of ammonium nitrate (solute), m₁ = 1.0 g
Mass of water (solvent), m₂ = 50.0 g
Initial temperature of water, T₁ = 25.0°C
Final temperature of water, T₂ = 23.32°C
First, let's calculate the moles of ammonium nitrate (NH4NO3):
Molar mass of NH4NO3 = 14.01 g/mol (N) + 4(1.01 g/mol) (H) + 3(16.00 g/mol) (O) = 80.04 g/mol
n = m₁ / Molar mass
n = 1.0 g / 80.04 g/mol = 0.0125 mol
Now, calculate the heat absorbed or released:
ΔT = T₂ - T₁
ΔT = 23.32°C - 25.0°C = -1.68°C
Note: We convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius value because the specific heat capacity of water is given in J/(g·K).
q = m₂ × c × ΔT
q = 50.0 g × 4.18 J/(g·K) × (-1.68 K)
q = -353.08 J
Finally, convert the heat from joules to kilojoules:
H = q / n
H = -353.08 J / 0.0125 mol
H = -28246.4 J/mol = -28.25 kJ/mol
Therefore, the molar heat of solution (H) for this reaction is -28.25 kJ/mol.
To find the molar heat of solution, we need to use the equation:
q = m x c x ΔT
where:
q = heat gained or lost (in joules)
m = mass of the substance (in grams)
c = specific heat capacity (in J/g°C)
ΔT = change in temperature (in °C)
First, let's calculate the heat gained or lost by the water using the equation above. Since the temperature decreased, the water lost heat during the process.
m(water) = 50.0 g (mass of water)
c(water) = 4.18 J/g°C (specific heat capacity of water, which is approximately 4.18 J/g°C)
ΔT = 23.32°C - 25.0°C (change in temperature)
Now, we can substitute these values into the equation to determine the heat lost by the water:
q(water) = m(water) x c(water) x ΔT
Next, we need to calculate the number of moles of ammonium nitrate used (NH4NO3):
m(NH4NO3) = 1.0 g (mass of ammonium nitrate)
M(NH4NO3) = molar mass of ammonium nitrate
The molar mass of NH4NO3 can be calculated by adding up the atomic masses of each element:
M(NH4NO3) = (1*1) + (4*1) + (14*1) + (3*16) = 80.05 g/mol
To find the heat lost per mole (molar heat of solution), we use the equation:
H = q(water) / n(NH4NO3)
where:
H = molar heat of solution (in J/mol)
n(NH4NO3) = moles of NH4NO3
Finally, we can divide the calculated heat lost by the moles of NH4NO3 to obtain the molar heat of solution in joules per mole (J/mol). To convert to kilojoules per mole (kJ/mol), we divide by 1000.
H(kJ/mol) = H(J/mol) / 1000
Let's plug in the numbers to calculate the molar heat of solution.