If 8.00 g of ammonuim nitrate is dissolved in 1000 ml of water for use as a plant fertilizer, the water decreases in temperature form 21.00C to 20.39 C. Determine the molar heat of solution of ammonium nitrate
q = mass water x specific heat water x delta T.
q/8.00 g = heat soln J/g
Convert that to heat soln J/mole using the molar mass of NH4NO3.
To determine the molar heat of solution of ammonium nitrate, we need to use the equation:
q = m * c * ΔT
where:
q is the heat absorbed or released during the reaction (in Joules)
m is the mass of the solute (in grams)
c is the specific heat capacity of the solution (in J/g·°C)
ΔT is the change in temperature (in °C)
First, we need to calculate the heat absorbed or released during the reaction using the given data.
ΔT = T2 - T1
= 20.39 °C - 21.00 °C
= -0.61 °C
Note: If the sign of ΔT is negative, it means heat is lost by the solution.
Now, we need to calculate the mass of the solute. Given that 8.00 g of ammonium nitrate is dissolved in 1000 mL of water, we need to convert mL to grams using the density of water.
Density of water = 1 g/mL
Mass of water = Volume of water * Density
= 1000 mL * 1 g/mL
= 1000 g
Thus, the mass of ammonium nitrate = 8.00 g
Next, we need to determine the specific heat capacity of the solution (c). Since it is a water solution, we can use the specific heat capacity of water.
c = 4.18 J/g·°C
Now, we can substitute the values into the equation:
q = m * c * ΔT
= 8.00 g * 4.18 J/g·°C * -0.61 °C
= -19.36 J
The heat transferred during the process is -19.36 J.
To calculate the molar heat of solution (ΔH) of ammonium nitrate, we need to convert the heat transfer to per mole of ammonium nitrate.
First, calculate the moles of ammonium nitrate:
moles = mass / molar mass
The molar mass of ammonium nitrate (NH4NO3):
(1 * 14.01 g/mol) + (4 * 1.01 g/mol) + (1 * 14.01 g/mol) + (3 * 16.00 g/mol) = 80.04 g/mol
moles = 8.00 g / 80.04 g/mol
= 0.100 mol
Finally, divide the heat transfer by the number of moles:
ΔH = q / moles
= -19.36 J / 0.100 mol
= -193.6 J/mol
Therefore, the molar heat of solution of ammonium nitrate is approximately -193.6 J/mol.