2. 50.0 mL of 1 M NaOH(aq) and 50.0 mL of 1 M HNO3(aq), both initially at 18.6°C, were mixed in a Styrofoam cup calorimeter. The temperature of the solution rose to 25.4°C. How much heat was released? Assume that the heat capacity and density of the solution are the same as water. Show all working.
heat released:.1kg*Cw*(25.4-18.6)
To find the amount of heat released, we first need to calculate the change in temperature (∆T) and then use it to calculate the amount of heat released using the formula:
Q = mc∆T
where:
Q = heat released (in joules)
m = mass of the solution (in grams)
c = specific heat capacity of the solution (assumed to be the same as water)
∆T = change in temperature (in Celsius)
Now, let's break down the steps to calculate the amount of heat released:
Step 1: Calculate the mass of the solution
Since we have equal volumes of NaOH and HNO3 solutions, we can assume that the densities of the two solutions are equal. Therefore, we can calculate the mass of the solution by multiplying the volume (50.0 mL) by the density of water.
Density of water = 1 g/mL
Mass of the solution = Volume × Density = 50.0 mL × 1 g/mL = 50.0 g
Step 2: Calculate the change in temperature (∆T)
∆T = Final temperature - Initial temperature = 25.4°C - 18.6°C = 6.8°C
Step 3: Calculate the amount of heat released (Q)
Now, we have all the necessary values to calculate the amount of heat released.
Specific heat capacity of water (c) = 4.18 J/g°C (This is an approximation since the specific heat capacity of the mixture may not be exactly the same as water, but it is a reasonable assumption.)
Q = mc∆T = 50.0 g × 4.18 J/g°C × 6.8°C = 1427.6 J
So, the amount of heat released is approximately 1427.6 Joules.