Final answer:
To calculate the number of grams of mg needed to release enough energy to increase the temperature of the water, we can use the equation: q = m*C*ΔT. Given the density of water and the volume of water, we can calculate the mass of water. Then, using the specific heat of water and the change in temperature, we can calculate the heat absorbed by the water.
Step-by-step explanation:
To calculate the number of grams of mg needed to release enough energy to increase the temperature of the water, we can use the equation:
q = m*C*ΔT
Where:
- q is the heat absorbed by the water
- m is the mass of the water
- C is the specific heat of water
- ΔT is the change in temperature
Given that the density of water is 0.997 g/ml and the volume of water is 78 ml, we can calculate the mass of water as:
m = density * volume
Substituting the values, we get:
m = 0.997 g/ml * 78 ml = 77.646 g
To calculate the heat absorbed by the water, we need to consider the change in temperature:
ΔT = final temperature - initial temperature
Substituting the values, we get:
ΔT = 78°C - 26°C = 52°C
Now we can calculate the heat absorbed by the water:
q = m * C * ΔT
Substituting the values of m, C, and ΔT, we get:
q = 77.646 g * 4.184 J/g °C * 52°C = 16,138.484 J
Since 1 kJ = 1000 J, we can convert the heat absorbed to kJ:
q = 16,138.484 J / 1000 = 16.138 kJ
Therefore, the number of grams of mg needed for this reaction to release enough energy to increase the temperature of 78 ml of water from 26 to 78 °C is approximately 16.138 grams.