Question

a tiny sample of an aqueous solution of two substances r and p is sketched below, as if it was under an imaginary microscope so powerful that individual molecules could be seen. (the water molecules are not shown.) r and p can interconvert. that is, r can turn into p, and p can turn back into r: r(aq)⇌p(aq) the equilibrium constant k for this equilibrium is 2. predict the number of r and p molecules in this sample when the interconversion reaches equilibrium. number of r molecules: number of p molecules: incorrect your answer is incorrect. try one last time

Explanation:

Step1: Define equilibrium - constant expression

The equilibrium - constant expression for the reaction $R(aq)
ightleftharpoons P(aq)$ is $K=\frac{[P]}{[R]}$, where $[P]$ and $[R]$ are the molar concentrations of $P$ and $R$ at equilibrium. Since the volume is the same for both $P$ and $R$, the ratio of the number of molecules of $P$ to $R$ is equal to the ratio of their concentrations. Let the number of $R$ molecules be $x$ and the number of $P$ molecules be $y$. Then $K = 2=\frac{y}{x}$. Also, assume the total number of molecules (either $R$ or $P$) in the sample is $N=x + y$.

Step2: Solve the system of equations

From $y = 2x$ and $N=x + y$, substitute $y$ in the second - equation: $N=x+2x=3x$. Count the total number of molecules in the sample. There are 12 molecules in the sample, so $N = 12$. Then $3x=12$, which gives $x = 4$ (number of $R$ molecules) and $y=8$ (number of $P$ molecules).

Answer:

Number of $R$ molecules: 4
Number of $P$ molecules: 8