The dissolution of ammonium nitrate in water changes the temperature of water from 21C to - 1C(ice). If the molar enthalpy of ammonium nitrate is 25.7kj/mol. Determine the mass of ammonium nitrate that was dissolved
To determine the mass of ammonium nitrate that was dissolved, we can use the equation:
ΔH = q / n
Where:
ΔH is the molar enthalpy change of ammonium nitrate (25.7 kJ/mol),
q is the heat absorbed or released by the water,
n is the number of moles of ammonium nitrate.
First, we need to calculate the heat absorbed or released by the water.
q = mcΔT
Where:
q is the heat absorbed or released by the water,
m is the mass of water,
c is the specific heat capacity of water,
ΔT is the change in temperature.
The specific heat capacity of water is approximately 4.18 J/g°C.
Now, let's calculate the heat absorbed or released by the water.
q = mcΔT
m = q / (cΔT)
= q / (4.18 J/g°C * (21°C - (-1°C)))
= q / (4.18 J/g°C * 22°C)
= q / 91.96 J/g
Now, let's substitute the heat absorbed or released by the water into the equation for calculating the number of moles of ammonium nitrate.
ΔH = q / n
n = q / ΔH
= (q / 91.96 J/g) / (25.7 kJ/mol * 1000 J/kJ)
= (q / 91.96 J/g) / 25.7 J/mol
= q / (25.7 * 91.96) mol/g
Assuming the density of ammonium nitrate is 1.725 g/mL, we can calculate the mass of ammonium nitrate dissolved.
Mass of ammonium nitrate = n * Molar mass of ammonium nitrate
Molar mass of ammonium nitrate = 80.0434 g/mol
Now, let's substitute the calculated value of n into the equation for calculating the mass of ammonium nitrate.
Mass of ammonium nitrate = (q / (25.7 * 91.96)) mol/g * 80.0434 g/mol
Please provide the value of q (the heat absorbed or released by the water) in order to determine the mass of ammonium nitrate dissolved.
To determine the mass of ammonium nitrate that was dissolved, we can use the concept of molar enthalpy and the equation:
ΔH = q / n
Where ΔH is the molar enthalpy, q is the heat absorbed or released, and n is the number of moles.
Firstly, let's calculate the heat released by the ammonium nitrate using the change in temperature of water:
q = mcΔT
Where q is the heat absorbed or released, m is the mass of water, c is the specific heat of water, and ΔT is the change in temperature.
Given:
Initial temperature (T1) = 21°C
Final temperature (T2) = -1°C
Specific heat of water (c) = 4.18 J/g°C (or 4.18 kJ/kg°C, since 1 g = 0.001 kg)
q = (m_water)(c)(ΔT)
q = (m_water)(4.18 kJ/kg°C)(-1°C - 21°C)
q = (m_water)(4.18 kJ/kg°C)(-22°C)
q = (m_water)(-91.96 kJ/kg)
Next, we calculate the number of moles of ammonium nitrate. Since the molar enthalpy is given in kJ/mol, we need to convert the units:
n = q / ΔH
n = (m_ammonium nitrate)(ΔH)
m_ammonium nitrate = n / ΔH
Substituting the values:
m_ammonium nitrate = (-91.96 kJ/kg) / (25.7 kJ/mol)
To obtain the mass, we need to consider the molar mass of ammonium nitrate (NH4NO3). The molar mass is calculated by adding up the atomic masses of the elements:
NH4NO3 = (1*14.01 g/mol N) + (4*1.01 g/mol H) + (3*16.00 g/mol O) = 80.05 g/mol
Finally, we can calculate the mass of ammonium nitrate dissolved:
m_ammonium nitrate = (-91.96 kJ/kg) / (25.7 kJ/mol) * (80.05 g/mol)
Please note that the final mass will be in grams.