When 1.51 g of NH4Cl are dissolved in 100. mL of water at 25.00C, the temperature drops to 23.98C. Calculate the molar enthalpy of dissolving (kJ/mol)
To calculate the molar enthalpy of dissolving, we can use the equation:
q = m∙C∙ΔT
Where:
- q is the heat absorbed or released in the reaction (in J)
- m is the mass of the substance being dissolved (in g)
- C is the specific heat capacity of water (4.184 J/g°C)
- ΔT is the change in temperature (in °C)
First, let's calculate the heat absorbed by the water:
q = (100. g)(4.184 J/g°C)(23.98°C - 25.00°C)
q = -200.84 J
Since the temperature drops, the heat is released by the system.
Next, we need to calculate the number of moles of NH4Cl:
moles = mass / molar mass
moles = 1.51 g / (14.01 g/mol + 1.01 g/mol + 4(1.01 g/mol))
moles = 0.1 mol
Now, let's calculate the molar enthalpy of dissolving:
ΔH = q / moles
ΔH = -200.84 J / 0.1 mol
ΔH = -2008.4 J/mol
The molar enthalpy of dissolving is -2008.4 J/mol. To convert it to kJ/mol, divide by 1000:
ΔH = -2008.4 J/mol / 1000
ΔH = -2.0084 kJ/mol
Therefore, the molar enthalpy of dissolving NH4Cl is approximately -2.0084 kJ/mol.
To calculate the molar enthalpy of dissolving, we can use the equation:
q = m × C × ΔT
Where:
q = heat flow (in Joules)
m = mass (in grams)
C = specific heat capacity (in J/g°C)
ΔT = change in temperature (in °C)
First, we need to calculate the heat flow (q) by using the equation:
q = m × C × ΔT
Given:
m = 1.51 g
C = specific heat capacity of water = 4.184 J/g°C
ΔT = 25.00°C - 23.98°C = 1.02°C
Now, calculate the heat flow:
q = 1.51 g × 4.184 J/g°C × 1.02°C = 6.72544 J
Next, we need to convert the heat flow from Joules (J) to kilojoules (kJ):
q = 6.72544 J = 0.00672544 kJ
To find the molar enthalpy of dissolving, we need to convert grams of NH4Cl to moles using the molar mass of NH4Cl.
The molar mass of NH4Cl is:
(1 × 14.01 g/mol) + (4 × 1.01 g/mol) + (1 × 35.45 g/mol) = 53.49 g/mol
Now, calculate the number of moles:
moles = mass / molar mass
moles = 1.51 g / 53.49 g/mol = 0.02824 mol
Finally, calculate the molar enthalpy of dissolving by dividing the heat flow by the number of moles:
molar enthalpy of dissolving = q / moles
molar enthalpy of dissolving = 0.00672544 kJ / 0.02824 mol ≈ 0.238 kJ/mol
Therefore, the molar enthalpy of dissolving NH4Cl is approximately 0.238 kJ/mol.
To calculate the molar enthalpy of dissolving, we can use the formula:
ΔH = q / n
where ΔH is the molar enthalpy of dissolving in kJ/mol, q is the heat transferred in Joules, and n is the moles of the solute.
First, let's calculate the heat transferred (q):
q = m * C * ΔT
where m is the mass of the water in grams, C is the specific heat capacity of water (4.18 J/g°C), and ΔT is the change in temperature.
We are given that 1.51 g of NH4Cl is dissolved in 100. mL of water at 25.00°C, and the temperature drops to 23.98°C.
To calculate the mass of water (m), we need to convert volume to mass using the density of water:
Density of water = 1.00 g/mL
m = volume * density
m = 100. mL * 1.00 g/mL
m = 100.00 g
Now we can calculate the heat transferred (q):
q = m * C * ΔT
q = 100.00 g * 4.18 J/g°C * (23.98°C - 25.00°C)
q = - 199 J (Note: negative sign indicates heat was released)
Next, we need to calculate the moles of NH4Cl (n) dissolved:
moles = mass / molar mass
The molar mass of NH4Cl is:
(1xN) + (4xH) + (1xCl) = 14.01 + 4(1.01) + 35.45 = 53.49 g/mol
moles = 1.51 g / 53.49 g/mol
moles ≈ 0.0282 mol
Now we can calculate the molar enthalpy of dissolving (ΔH):
ΔH = q / n
ΔH = - 199 J / 0.0282 mol
ΔH ≈ - 7046 J/mol
To convert to kJ/mol, divide by 1000:
ΔH ≈ - 7.046 kJ/mol
Therefore, the molar enthalpy of dissolving NH4Cl is approximately -7.046 kJ/mol.