Question

Complete the following table of data for Na₂HAsO₄. (Assume the density of water is 1.00 g/mL.)

T (°C)	Solubility (g/100. g)	Concentration (M)	Ksp	ΔG (kJ/mol)
42.0	49.0	?	?	?
48.0	54.9	?	?	?
54.0	60.8	?	?	?
60.0	66.8	?	?	?
66.0	72.7	?	?	?
72.0	78.6	?	?	?
78.0	84.5	?	?	?

Use a graph of ΔG vs. T to determine the following. (Enter your answers to three significant figures.)

What is the value of ΔH for the system?(in kJ/mol)

What is the value of ΔS for the system? (in J/mol·K)

Answer 1

Na₂HAsO₄ dissociates as

Na₂HAsO₄ 2 Na⁺ + HAsO₄^-

hence, Ksp = [Na⁺ ] ²* [ HAsO₄^-]

let molar solubility of Ksp = S (M)

then [Na⁺ ] = 2S (M ) and  [ HAsO₄^-] = s (M)

hence,

Ksp = (2S)²* S = 4s³ M³

Molar mass of Na₂HAsO₄ = 185.9 g/mol

then,

molarity = (mass of Na₂HAsO₄ * 1000) / (molar mass of Na₂HAsO₄ * volume of water )

density is 1.00 g/L , hence mass of water = volume of water.

molar concentration (M) , Ksp and   at different temperature are calculated below

42⁰ c

M = 49*1000/185.90*100 = 2.647

Ksp = 4*(2.647)³ = 74.21 M³

= - RTl n Ksp = -8.314*(42+273) ln 74.21 = - 11279.38 J = -11.279 KJ/mol

48⁰ c

M = 54.9*1000/185.90*100 = 2.966

Ksp = 4*(2.966)³ = 10.4.36 M³

= - RTln Ksp = -8.314*(48+273) ln 104.36 = -12404.144 J = -12.40 KJ/mole

54⁰ c

M = 60.8*1000/185.90*100 = 3.284

ksp =4*(3.284)³ = 141.66

= - RTln Ksp = -8.314*(54+273) ln 104.36 = -12635.99 J = -12.63 KJ/mole

60⁰ c

M = 66.8*1000/185.90*100 = 3.609

ksp = 4*(3.609)³ = 188.02 M³

= - RTlnKsp = -8.314*(60+273) ln 188.02 = - 14497.70 J = -14.49 KJ/mole

66⁰ c

M = 72.7*1000/185.09*100 = 3.927

Ksp = 4*(3.927)³ = 242.23 M³

= - RTlnKsp = -8.314*(66+273) ln 242.23 = -15472.95 J = -15.472 KJ/mole

72⁰ c

M = 78.6*1000/185.09*100 = 4.246

Ksp = 4*(4.246)³ = 306.19 M³

= - RTlnKsp = -8.314*(72+273) ln 306.19 = - 16418.911 J = -16.41 KJ/mole

78⁰ c

M = 84.5*1000/185.09*100 = 4.56

Ksp = 4*(4.56)³ = 379.275 M³

= - RTlnKsp = - 8.314*(78+273) ln 379.275 = -17329.11 J = -17.32 KJ/mole

now plot of vs T

the bestline equation is

y = -172.7 x +43222

comparing with the equation

= - T

where. slope = = 172.7 J/mol

and = intercept = 43222 KJ/mole = 43.22 KJ/mole