When 3.50 g of Ba(s) is added to 100.00 g of water in a container open to the atmosphere, the reaction shown below occurs and the temperature of the resulting solution rises from 22.00°C to 47.40°C. If the specific heat of the solution is 4.18 J/(g °C), calculate the heat absorbed by the solution.
A
15.9 kJ
B
5.3 kJ
C
2.1 kJ
D
10.6 kJ
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1
Identify the reaction taking place: Ba(s) + 2H2O(l) → Ba(OH)2(aq) + H2(g). This is an exothermic reaction, meaning it releases heat.
Determine the mass of the solution. Since the mass of water is 100.00 g and the mass of Ba is 3.50 g, the total mass of the solution is 100.00 g + 3.50 g = 103.50 g.
Calculate the change in temperature (ΔT) of the solution. The initial temperature is 22.00°C and the final temperature is 47.40°C, so ΔT = 47.40°C - 22.00°C.
Use the formula for heat absorbed or released: q = m × c × ΔT, where q is the heat absorbed, m is the mass of the solution, c is the specific heat capacity, and ΔT is the change in temperature.
Substitute the known values into the formula: m = 103.50 g, c = 4.18 J/(g °C), and ΔT is the temperature change calculated in the previous step. Solve for q to find the heat absorbed by the solution.