A 64.0 mL sample of 1.0 M NaOH is mixed with 47.0 mL of 1.0 M H2SO4 in a large S

Question

A 64.0 mL sample of 1.0 M NaOH is mixed with 47.0 mL of 1.0 M H2SO4 in a large Styrofoam coffee cup; the cup is fitted with a lid through which passes a calibrated thermometer. The temperature of each solution before mixing is 22.6 °C. After adding the NaOH solution to the coffee cup, the mixed solutions are stirred until reaction is complete. Assume that the density of the mixed solutions is 1.0 g/mL, that the specific heat of the mixed solutions is 4.18 J/(g •°C), and that no heat is lost to the surroundings. The rxn for the neutralization of NaOH with H2SO4 is –114 kJ/mol H2SO4. What is the maximum measured temperature in the Styrofoam cup?

Explanation / Answer

(64.0 mL) x (1.0 M NaOH) = 64.0 mmol NaOH

(47.0 mL) x (1.0 M H2SO4) = 47.0 mmol H2SO4

2 NaOH + H2SO4 Na2SO4 + 2 H2O

64.0 mmoles of NaOH would react completely with 64.0 x (1/2) = 32 mmoles of H2SO4, but there is more H2SO4 present than that, so H2SO4 is in excess and NaOH is the limiting reactant.

(0.032 mol H2SO4) x (-114 kJ/mol H2SO4) = 3648 J produced by the reaction and absorbed by the water

Supposing additive volumes:
(3648 J) / (4.18 J/(g·°C)) / ((64.0 mL + 47.0 mL) x (1.00 g/mL)) = 7.86°C change

22.6°C + 7.86°C = 30.46°C

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