If $$k=\frac{ 1 }{0.13 }$$ (where the "1" in the numerator is an exact number in a mathematical formula), enter the value of ln K.

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photon336 · Answer

First step is to rewrite this .13 = 13/100 you'll see why 

$$k = \frac{ 1 }{ 0.13 } =  \frac{ 1 }{ \frac{ 13 }{ 100} }$$

We simplify by multiplying both the numerator and denominator by 100. 

$$\frac{ 1*(100) }{ \frac{ 13 }{ 100 }*(100) }$$

which gives us the following. 

$$k  = \frac{ 100 }{ 13  }  = 7.7$$

This is the value of K not Ln{k} 

what this all means. we take our reaction right, k gives us the ratio of the products to the reactants those brackets around them mean the concentration of the reactants and products.  

$$A+B \rightarrow C + D ;  k = \frac{ [D][C] }{ [A][B] }; \frac{ [Products] }{ [Reactants] }$$

the value of K at equilibrium means whether the products or reactants are favored and the overall direction the reaction will lie. 

$$k > 1 favors products ; k <1 favors reactants. $$

of course now that we have the value of K which is 7.7 

all we need to do now is figure out what ln(k) is. 

$$\ln 7.7= 2.1$$

The spontaneity of the reaction, sign of delta G, determines whether the reaction is spontaneous. Spontaneity means whether the reaction will happen or not under the said temperature. it does not say how fast or slow it will be. 

Ln(K) will be greater than zero positive if the value of k is greater than 1. this makes sense a positive large value for k will result in a negative value for delta G and hence the reaction will be spontaneous.  RT we can just treat those as constants.  

if K  < 1 Ln(K) will be negative which implies that the forward reaction is not spontaneous. this means that at equilibrium a K < 1 means that the reactants are favored at equilibrium not the products, implying that the forward reaction is not spontaneous when we look at the formula below.

$$\Delta G = -RtLnK$$