Instant cold packs, often used to ice athletic injuries on the field, contain ammonium nitrate and water separated by a thin plastic divider. When the divider is broken, the ammonium nitrate dissolves according to the following endothermic reaction:
In order to measure the enthalpy change for this reaction, 1.25 of is dissolved in enough water to make 25.0 of solution. The initial temperature is 25.8 and the final temperature (after the solid dissolves) is 21.9 .
Calculate the change in enthalpy for the reaction. (Use as the density of the solution and as the specific heat capacity.)
1.25 what?
25.0 what?
25.8 what?
21.9 what?
Also the sentence in parentheses omits the density and specific heat of water to be used.
The following is how the problem is solved after you plug in the right units.
q = mass H2O x specific heat H2O x delta T
q/grams = delta H/gram and
(delta H in J/g) x molar mass NH4NO3 = delta H in J/mol.
To calculate the change in enthalpy for the reaction, we can use the equation:
ΔH = q / moles
First, we need to calculate the moles of ammonium nitrate (NH4NO3) by using its molar mass (80.0434 g/mol) and the mass provided (1.25 g):
moles = mass / molar mass
moles NH4NO3 = 1.25 g / 80.0434 g/mol
Next, we need to calculate the heat absorbed by the solution (q) using the equation:
q = mass solution × specific heat capacity × ΔT
where:
- mass solution is the mass of the solution, given as 25.0 g
- specific heat capacity is given as 4.18 J/g°C
- ΔT is the change in temperature, given as T final - T initial
Substituting the given values:
q = 25.0 g × 4.18 J/g°C × (21.9°C - 25.8°C)
Now, we can calculate the change in enthalpy:
ΔH = q / moles NH4NO3
Substituting the calculated values:
ΔH = q / (1.25 g / 80.0434 g/mol)
Now, we can proceed with the calculations:
ΔH = (25.0 g × 4.18 J/g°C × (21.9°C - 25.8°C)) / (1.25 g / 80.0434 g/mol)
To calculate the change in enthalpy for the reaction, we need to use the formula:
ΔH = q / n
where:
ΔH is the change in enthalpy,
q is the heat absorbed or released by the system, and
n is the number of moles of the substance involved in the reaction.
To find the heat absorbed or released (q), we can use the formula:
q = mcΔT
where:
m is the mass of the solution,
c is the specific heat capacity of the solution, and
ΔT is the change in temperature.
First, let's calculate the mass of the solution:
We are given that 1.25 g of NH4NO3 is dissolved in enough water to make 25.0 g of solution. So, the mass of the solution is 25.0 g.
Next, let's calculate the change in temperature (ΔT):
ΔT = final temperature - initial temperature
ΔT = 21.9°C - 25.8°C
ΔT = -3.9°C
The negative sign indicates a decrease in temperature.
Now, let's calculate the heat absorbed or released (q):
q = mcΔT
Given:
m = 25.0 g
c = specific heat capacity (not provided)
ΔT = -3.9°C
Since the specific heat capacity (c) is not provided, we cannot calculate the exact value of q. The specific heat capacity of the solution depends on its composition.