In an experiment, 95.0 mL of 0.225 M silver nitrate was mixed rapidly with 47.5 mL of 0.225 M calcium chloride in a coffee cup calorimeter. If a reaction occurred, was it exothermic or endothermic? If the reaction started at 23.7 °C, what is the final temperature of the solution?
To determine whether the reaction is exothermic or endothermic, we need to compare the initial and final temperatures. If the final temperature is higher than the initial temperature, it indicates an exothermic reaction (heat is released). If the final temperature is lower than the initial temperature, it indicates an endothermic reaction (heat is absorbed).
To find the final temperature, we can use the equation:
q = m * C * ΔT
where:
q is the heat transferred (in joules),
m is the mass of the solution (in grams),
C is the specific heat capacity of the solution (in J/g°C),
and ΔT is the change in temperature (final temperature - initial temperature).
Since the specific heat capacity of the solution depends on the composition, we can assume it to be around 4.18 J/g°C, which is typical for aqueous solutions.
First, let's find the mass of the solution. To do this, we'll need the density of water, which is 1 g/mL.
Mass of silver nitrate solution (m1) = volume of silver nitrate solution * density of water
= 95.0 mL * 1 g/mL
= 95.0 g
Mass of calcium chloride solution (m2) = volume of calcium chloride solution * density of water
= 47.5 mL * 1 g/mL
= 47.5 g
Total mass of the solution (m) = mass of silver nitrate solution + mass of calcium chloride solution
= m1 + m2
= 95.0 g + 47.5 g
= 142.5 g
Now, let's calculate the heat transferred (q) using the equation mentioned earlier.
q = m * C * ΔT
Since the heat transferred is the same for both reactants, we can equate their expressions.
m1 * C * (Tf - Ti) = m2 * C * (Tf - Ti)
Substituting the values we have:
95.0 g * 4.18 J/g°C * (Tf - 23.7 °C) = 47.5 g * 4.18 J/g°C * (Tf - 23.7 °C)
Let's solve this equation to find the final temperature (Tf).
95.0 g * (Tf - 23.7 °C) = 47.5 g * (Tf - 23.7 °C)
95Tf - 2251.5 = 47.5Tf - 1124.75
95Tf - 47.5Tf = -1124.75 + 2251.5
47.5Tf = 1126.75
Tf = 1126.75 / 47.5
Tf ≈ 23.7 °C
Since the final temperature (Tf) is approximately equal to the initial temperature (23.7 °C), we can conclude that no significant heat was exchanged during the reaction. Therefore, the reaction is classified as neither exothermic nor endothermic.