When 5.50 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 61.16°C.If the specific heat of the solution is 4.18 J/(g ∙ °C),calculate for the reaction,as written. Ba(s)+ 2 H₂O(l)→ Ba(OH)₂(aq)+ H₂(g) = ?

Question

Quizplus · Accepted Answer

First, we need to calculate the amount of heat absorbed by the solution using the formula:

q = mCΔT

where

q = amount of heat absorbed by the solution (in J) 
m = mass of the solution (in g) 
C = specific heat of the solution (in J/(g ∙ °C)) 
ΔT = change in temperature of the solution (in °C)

We have:

m = 100.00 g (mass of water) + 5.50 g (mass of Ba) = 105.50 g 
C = 4.18 J/(g ∙ °C) 
ΔT = 61.16°C - 22.00°C = 39.16°C

Plugging in the values, we get:

q = (105.50 g)(4.18 J/(g ∙ °C))(39.16°C) = 17325.17 J

Notice that this value is the amount of heat absorbed by the solution, not the amount of heat released by the reaction. To get the latter, we need to use the fact that the reaction is exothermic (it releases heat), and that the heat released is equal in magnitude but opposite in sign to the heat absorbed by the solution. In other words:

q(reaction) = - q(solution)

So the answer is:

q(reaction) = -17325.17 J = -17.33 kJ

Note that the answer is negative because the reaction releases heat (it is exothermic), so the sign of the answer should be negative. However, the answer choices are given in kJ (not J), so we need to convert our answer to kJ:

q(reaction) = -17.33 kJ

Finally, we round our answer to two decimal places and obtain:

q(reaction) = -17.33 kJ ≈ -17.3 kJ

Therefore, the correct answer is A (-431 kJ).

When 550 G of Ba(s)is Added to 100