3grams of ammonium chloride has been added to 20mL of water. The initial temperature of the solutionis 18.0 degrees, and once the ammonium is added to the water, the temperature declines to 11 degrees. Given the following information, calculate the enthalpy of solution per mole of ammonium chloride, and explain why the solution is exothermic.
Givens: mass of cup= 1.74g
Mass of cup+water= 21.92g
Mass of cup+h20+NH4Cl= 24.88g
Specific heat capacity of NH4Cl=1.57
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To calculate the enthalpy of solution per mole of ammonium chloride, we need to use the following formula:
ΔH = q / n
where ΔH is the enthalpy of solution per mole of ammonium chloride, q is the heat released or absorbed by the solution, and n is the number of moles of ammonium chloride.
First, let's calculate the heat released or absorbed by the solution (q) using the formula:
q = mcΔT
where m is the mass of the solution (in grams), c is the specific heat capacity of NH4Cl (in J/g°C), and ΔT is the change in temperature (in °C).
Given data:
Mass of cup = 1.74g
Mass of cup + water = 21.92g
Mass of cup + H20 + NH4Cl = 24.88g
Initial temperature (Ti) = 18.0°C
Final temperature (Tf) = 11.0°C
Specific heat capacity of NH4Cl = 1.57 J/g°C
First, we need to calculate the mass of the water:
Mass of water = Mass of cup + water - Mass of cup
= 21.92g - 1.74g
= 20.18g
Next, we need to calculate the mass of ammonium chloride:
Mass of NH4Cl = Mass of cup + H20 + NH4Cl - Mass of cup + water
= 24.88g - 21.92g
= 2.96g
Now we can calculate the heat released by the solution:
q = (20.18g)(1.57 J/g°C)(11.0°C - 18.0°C)
= (20.18g)(-10.99 J/g)
= -222.34 J (since the temperature decreases, the value is negative)
Next, we need to calculate the number of moles of ammonium chloride:
Number of moles = Mass of NH4Cl / Molar mass of NH4Cl
The molar mass of NH4Cl can be found by adding the atomic masses of nitrogen (N) and four hydrogen (H) atoms and chloride ion (Cl).
Molar mass of NH4Cl = (1 x Atomic mass of N) + (4 x Atomic mass of H) + Atomic mass of Cl
= (1 x 14.01 g/mol) + (4 x 1.01 g/mol) + 35.45 g/mol
= 53.49 g/mol
Number of moles = 2.96g / 53.49 g/mol
= 0.055 moles
Finally, we can calculate the enthalpy of solution per mole of ammonium chloride:
ΔH = q / n
= -222.34 J / 0.055 moles
= -4042 J/mol (rounded to the nearest whole number)
Explanation for the solution being exothermic:
The negative value for ΔH indicates an exothermic process, meaning that the solution releases heat to the surroundings. In this case, when ammonium chloride is dissolved in water, it releases energy in the form of heat. This is because the strength of the attractions between the water molecules and the ions in ammonium chloride is greater than the strength of the attractions between the ammonium and chloride ions within the solid compound. As a result, energy is released as the solid ammonium chloride breaks up and dissolves, leading to a decrease in temperature.