Calculate the final temperature of the mixture. (You may use the area below for

Question

Calculate the final temperature of the mixture. (You may use the area below for work; report only your answer.) Solve the following problems in the boxes provided with each question. Be sure to show all your work, including units and conversion factors, and round your answers to the appropriate significant figures. You may omit mL rightarrow Land mL rightarrow g conversion factors. 50.0 mL of 0.200 M NaOH is completely neutralized with 50.0 mL of HNO_3 in a coffee cup calorimeter. For these solutions, the densities are 1.00 g/mL, the initial temperatures are both 24.61 degree C, and the specific heat of the solution is 4.184 J/g degree C. If the final temperature of the solution is 25.95 degree C, calculate delta H_rxn, in kJ/mol, for the neutralization reaction: NaOH(aq) +HNO_3(aq) NaNO_3(aq) +H_2O(I)

Explanation / Answer

CALCULATION :

HNO3(aq) is a strong monoprotic acid: HNO3 H+(aq) + NO3-(aq)
NaOH(aq) is a strong monobasic base: NaOH Na+(aq) + OH-(aq)

VNaOH = Volume of NaOH = 50ml, MNaOH = 0.2 M

VHNO3 = Volume of HNO3 = 50ml, MHNO3= 0.2 M { Since M1V1 = M2V2 for acid base reactions }

Ti = Initial Temperature of Solution = 24.61oC

Tf = final temperature of solution at neutralisation = 25.95 oC

d = density of solutions = 1 g mL-1
Cg = specific heat capacity of solutions = 4.18 JoC-1g-1
q = heat liberated during neutralisation reaction (J)

since density = 1 g mL-1: 1 x volume (mL) = mass (g)
mass(NaOH) = 50.0 g
mass(HNO3) = 50.0 g

q = mtotal x Cg x T

mtotal = mass(NaOH) + mass(HNO3) = 50.0 + 50.0 = 100.0 g
Cg = 4.18 JoC-1g-1
T = Tf - Ti = 25.95 - 24.61 = 1.34 oC

q = 100.0 x 4.184 x 1.34 = 560.656 J

OH-(aq) + H+(aq) H2O(l)
1 mol OH-(aq) + 1 mol H+(aq) 1 mol H2O
moles(H2O) = moles(OH-(aq))
moles(OH-(aq)) = concentration (mol L-1) x volume (L) = 0.2 x 50/1000 = 0.01 mol
moles of water produced = 0.01 mol

H will be negative because the reaction is exothermic
H = heat liberated per mole of water = - q / moles of water
H = -560.656 / 0.01 = -56065.6 J mol-1

We can convert J to kJ by dividing by 1000:
H = -56065.6/ 1000 = -56.066 kJ mol-1

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