When 2.50 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 40.32 °C. If the specific heat of the solution is 4.18 J , calculate for the reaction, as written. Ba(s) + 2H₂O(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 is the amount of heat absorbed, m is the mass of the solution, C is the specific heat of the solution, and ΔT is the change in temperature.

m = 100.00 g (mass of water)
C = 4.18 J/g°C (specific heat of water)
ΔT = 40.32°C - 22.00°C = 18.32°C

q = (100.00 g)(4.18 J/g°C)(18.32°C) = 7670.496 J = 7.67 kJ

Next, we need to calculate the moles of Ba used in the reaction:

n(Ba) = m(Ba) / M(Ba)

where n(Ba) is the moles of Ba, m(Ba) is the mass of Ba, and M(Ba) is the molar mass of Ba.

m(Ba) = 2.50 g
M(Ba) = 137.33 g/mol

n(Ba) = (2.50 g) / (137.33 g/mol) = 0.0182 mol

From the balanced chemical equation, we can see that the reaction produces 1 mole of gas, so the reaction enthalpy can be calculated as:

ΔH = q / n(Ba)

ΔH = (7.67 kJ) / (0.0182 mol) = -421.15 kJ/mol

Since the reaction is exothermic (the temperature of the solution increased), the sign of ΔH is negative. Therefore, the correct answer is A) -431 kJ.

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