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4 years ago

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ΔG o for the reaction H2(g) + I2(g) ⇌ 2HI(g) is 2.60 kJ/mol at 25°C. Calculate ΔG o , and predict the direction in which the rea

ction is spontaneous. The initial pressures are: PH2 = 3.10 atm PI2 = 1.5 atm PHI 1.75 atm ΔG o = The reaction is spontaneous in the forward direction. The reaction is spontaneous in the reverse direction. Cannot be determined.

1 answer:

kondaur [170]4 years ago

4 0

Answer:

The reaction is not spontaneous in the forward direction, but in the reverse direction.

Explanation:

<u>Step 1: </u>Data given

H2(g) + I2(g) ⇌ 2HI(g) ΔG° = 2.60 kJ/mol

Temperature = 25°C = 25+273 = 298 Kelvin

The initial pressures are:

pH2 = 3.10 atm

pI2 = 1.5 atm

pHI 1.75 atm

<u>Step 2</u>: Calculate ΔG

ΔG = ΔG° + RTln Q

with ΔG° = 2.60 kJ/mol

with R = 8.3145 J/K*mol

with T = 298 Kelvin

Q = the reaction quotient → has the same expression as equilibrium constant → in this case Kp = [p(HI)]²/ [p(H2)] [p(I2)]

with pH2 = 3.10 atm

pI2 = 1.5 atm

pHI 1.75 atm

Q = (3.10²)/(1.5*1.75)

Q = 3.661

ΔG = ΔG° + RTln Q

ΔG = 2600 J/mol + 8.3145 J/K*mol * 298 K * ln(3.661)

ΔG =5815.43 J/mol = 5.815 kJ/mol

To be spontaneous, ΔG should be <0.

ΔG >>0 so the reaction is not spontaneous in the forward direction, but in the reverse direction.

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Answer : The correct possible mechanisms for the reaction is:

Step 1 : $X_2Y+Z_2\rightarrow X_2YZ_2$ (slow)

Step 2 : $X_2YZ_2+X_2Y\rightarrow 2X_2YZ$ (fast)

Explanation :

Rate law : It is defined as the expression which expresses the rate of the reaction in terms of molar concentration of the reactants with each term raised to the power their stoichiometric coefficient of that reactant in the balanced chemical equation.

As we are given the overall reaction,

$2X_2Y+Z_2\rightarrow 2X_2YZ$

The given expression of rate law for this reaction is,

$Rate=k[X_2Y][Z_2]$

Now we have to determine the possible mechanisms for the reaction.

The rate law expression for overall reaction should be in terms of $X_2Y$ and $Z_2$ .

As we know that the slow step is the rate determining step.

<u>Option 1 :</u>

Step 1 : $2X_2Y+Z_2\rightarrow 2X_2YZ$ (slow)

The expression of rate law for this reaction will be,

$Rate=k[X_2Y]^2[Z_2]$

<u>Option 2 :</u>

Step 1 : $X_2Y+Z_2\rightarrow X_2YZ+Z$ (fast)

Step 2 : $X_2Y+Z\rightarrow X_2YZ$ (slow)

The rate law from the slow step 2 is,

$Rate=K'[X_2Y][Z]$ .............(1)

Now applying steady state approximation for $Z$ , we get:

$\frac{d[Z]}{dt}=K"[X_2Y][Z_2]$ .........(2)

Now put equation 2 in 1, we get:

$Rate=K'K"[X_2Y]^2[Z_2]$

$K'K"=K$

The rate law expression will be:

$Rate=K[X_2Y]^2[Z_2]$

<u>Option 3 :</u>

Step 1 : $X_2Y+Z_2\rightarrow X_2YZ_2$ (slow)

Step 2 : $X_2YZ_2+X_2Y\rightarrow 2X_2YZ$ (fast)

The expression of rate law for this reaction will be,

$Rate=k[X_2Y][Z_2]$

<u>Option 4 :</u>

Step 1 : $2X_2Y\rightarrow X_4Y_2$ (fast)

Step 2 : $X_4Y_2+Z_2\rightarrow 2X_2YZ$ (slow)

The rate law from the slow step 2 is,

$Rate=K'[X_4Y_2][Z_2]$ .............(1)

Now applying steady state approximation for $X_4Y_2$ , we get:

$\frac{d[X_4Y_2]}{dt}=K"[X_2Y]^2$ .........(2)

Now put equation 2 in 1, we get:

$Rate=K'K"[X_2Y]^2[Z_2]$

$K'K"=K$

The rate law expression will be:

$Rate=K[X_2Y]^2[Z_2]$

<u>Option 5 :</u>

Step 1 : $Z_2\rightarrow Z+Z$ (slow)

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The rate law expression will be:

$Rate=K[Z_2]$

From the given options we conclude that the only option 3 is the correct possible mechanisms for the given reaction.

Hence, the correct possible mechanisms for the reaction is:

Step 1 : $X_2Y+Z_2\rightarrow X_2YZ_2$ (slow)

Step 2 : $X_2YZ_2+X_2Y\rightarrow 2X_2YZ$ (fast)

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