Let's address the problem step-by-step.
1. Identify Initial Concentrations:
- The concentration of [tex]\( \text{PCl}_3(g) \)[/tex] is increased to 1.2 M.
- The concentration of [tex]\( \text{PCl}_5(g) \)[/tex] and [tex]\( \text{Cl}_2(g) \)[/tex] are both initially assumed to remain constant at 1 M each.
2. Set Up the Reaction Ratio:
- The equilibrium expression (before disruption) involves the ratio of the concentration of [tex]\( \text{PCl}_5(g) \)[/tex] to the product of the concentrations of [tex]\( \text{PCl}_3(g) \)[/tex] and [tex]\( \text{Cl}_2(g) \)[/tex].
The formula is:
[tex]\[
\frac{\left[ \text{PCl}_5 \right]}{\left[ \text{PCl}_3 \right] \cdot \left[ \text{Cl}_2 \right]}
\][/tex]
3. Substitute the Given Values:
- [tex]\(\left[ \text{PCl}_5 \right] = 1 \text{ M}\)[/tex]
- [tex]\(\left[ \text{PCl}_3 \right] = 1.2 \text{ M}\)[/tex]
- [tex]\(\left[ \text{Cl}_2 \right] = 1 \text{ M}\)[/tex]
Plug these values into the expression:
[tex]\[
\frac{1}{(1.2) \cdot (1)}
\][/tex]
4. Perform the Calculation:
Simplify the denominator:
[tex]\[
1.2 \cdot 1 = 1.2
\][/tex]
Therefore, the ratio is:
[tex]\[
\frac{1}{1.2} \approx 0.83
\][/tex]
5. Express the Answer:
- Since the ratio must be expressed with two significant figures, the final answer is:
[tex]\[
0.83
\][/tex]
So, the ratio of products to reactants, given the increase in the concentration of [tex]\( \text{PCl}_3(g) \)[/tex] to 1.2 M, is:
[tex]\[
\boxed{0.83}
\][/tex]
