At 80.°C, Kc = 1.87 10-3 for the reaction.

PH3BCl3(s) PH3(g) + BCl3(g)
(a) Calculate the equilibrium concentrations of PH3 and BCl3 if a solid sample of PH3BCl3 is placed in a closed vessel at 80.°C and decomposes until equilibrium is reached.
(b) If the flask has a volume of 0.450 L, what is the minimum mass of PH3BCl3(s) that must be added to the flask in order to achieve equilibrium?

Kc=[PH3][BCl3]

since those are both equal concentratons, then

x^2=Kc
x= sqrt Kc

b. mass of PH3+massBCl3=2xVolume=2*.450*sqrtKc

thnx :)

why do both PH3 and BCL3 have equal concentrations at equilibrium?

Same leading digit, one mole each

To answer part (a) of the question, we can use the equilibrium constant expression (Kc) and the balanced equation for the reaction. The equilibrium constant expression for this reaction is:

Kc = [PH3(g)] * [BCl3(g)] / [PH3BCl3(s)]

Given that Kc = 1.87 * 10^-3 and that we have a solid sample of PH3BCl3, we know that initially the concentrations of PH3 and BCl3 will be 0. However, the concentration of PH3BCl3 will not change, as it is in the solid state.

Let's assume that x mol of PH3(g) and BCl3(g) are produced at equilibrium. Since the moles of PH3 and BCl3 are both equal to x, we can write the equilibrium concentration of PH3(g) as [PH3(g)] = x/V, and the equilibrium concentration of BCl3(g) as [BCl3(g)] = x/V, where V is the volume of the flask (0.450 L).

Using the equilibrium constant expression, we can substitute the equilibrium concentrations of PH3(g) and BCl3(g) into the expression:

1.87 * 10^-3 = (x/V) * (x/V) / [PH3BCl3(s)]

To solve this equation, we need to know the initial concentration of PH3BCl3, which is not provided in the question.

Now let's move on to part (b) of the question. To determine the minimum mass of PH3BCl3(s) that must be added to the flask to achieve equilibrium, we need to consider the stoichiometry of the reaction.

According to the balanced equation: 1 mol of PH3BCl3(s) decomposes to produce 1 mol of PH3(g) and 1 mol of BCl3(g).

Using the ideal gas law, we can convert volume (V) to moles (n) for PH3(g) and BCl3(g) at the given conditions (80.°C). After calculating the moles of PH3(g) and BCl3(g) at equilibrium (x), we can multiply it by the molar mass of PH3BCl3 to determine the minimum mass required.

However, without the initial concentration or mass of PH3BCl3, we cannot calculate the minimum mass required in part (b).

In summary, to answer part (a) of the question, we need the initial concentration of PH3BCl3, which is not provided. For part (b), we need the initial mass of PH3BCl3, which is also not given.