A student mixes two aqueous solutions, whose masses are 30.0 g and 35.0 g, together. Each solution is initially at a temperature of 25.0°C. Upon mixing the solutions, a chemical reaction occurs. The final solution has a temperature of 30.0°C. What is the heat change, in kJ, for this reaction?
a) 5.25 kJ
b) 1360 kJ
c) 1.36 kJ
d) 1.95 kJ
So the final solution is 65 g that has changed T from 25.0 to 30.0.
q = mass x specific heat x (Tfinal - Tinitial)
q = 65 x 4.18 J/g*C x (Tfinal - Tinitial)
Convert to kJ.
To find the heat change for this reaction, we can use the principle of heat transfer, which states that the heat gained by one substance is equal to the heat lost by another substance in a chemical reaction.
The heat gained or lost by a substance can be calculated using the equation:
Q = m * c * ΔT
Where:
Q is the heat change (in joules)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in J/g°C)
ΔT is the change in temperature (in °C)
First, let's calculate the heat change for the first solution:
Q1 = m1 * c * ΔT1
Q1 = 30.0 g * c * (30.0°C - 25.0°C)
Next, let's calculate the heat change for the second solution:
Q2 = m2 * c * ΔT2
Q2 = 35.0 g * c * (30.0°C - 25.0°C)
Since the heat gained by one substance is equal to the heat lost by another substance, we can set Q1 + Q2 equal to zero:
Q1 + Q2 = 0
Substituting the values we have:
30.0 g * c * (30.0°C - 25.0°C) + 35.0 g * c * (30.0°C - 25.0°C) = 0
Simplifying the equation:
(c * 150.0 g * 5.0°C) + (c * 175.0 g * 5.0°C) = 0
c * 150.0 g * 5.0°C + c * 175.0 g * 5.0°C = 0
c * 1250.0 g * °C = 0
Now, let's solve for c to determine the specific heat capacity:
c = 0 / (1250.0 g * °C)
c = 0
Since c = 0, it means that the specific heat capacity of the solution is zero. This indicates that the solution does not absorb or release any heat during the reaction.
Therefore, the heat change for this reaction is 0 kJ. So neither a), b), c), nor d) is the correct answer.