For the decomposition reaction PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), K_p = 381 at 600 K and K_c = 46.9 at 700 K. (b) If 1.25 g of PCl₅ is introduced into an evacuated 0.500-L flask at 700 K and the decomposition reaction is allowed to reach equilibrium, what percent of the PCl₅ will decompose and what will be the total pressure in the flask?

Video transcript

Hello. In this problem we are told the equilibrium constant in terms of concentration at 500 Kelvin and equilibrium constant in terms of pressure. 400 Kelvin for the following decomposition reaction are 49.3 and 397. Respectfully And 500 Kelvin, 1.78 g of vinyl chloride are placed in a 1.5 liter flask and allowed to reach equilibrium. We are asked what percentage of the 1.78 g of spinal cord will decompose at 500 Kelvin. And what is the total pressure in the flask? Let's begin by finding the concentration of the vinyl chloride. We have 1.78 g. That's diana chloride And 1.5 L flasks. We'll make use of the molar mass convert from mass two moles, One mole of vinyl chloride has a mass of .970 g. They set up remote mass so that our grams cancel. And so this works out to 0. Molar. Now let's create an ice table. So while we have our decomposition reaction and then we have initial change in equilibrium. Initially. Then we have 0.009973 Mueller vinyl chloride and initially no products present. The change then is minus X. And then plus X. And plus X. Our equilibrium we're combining the initial and the change of 0.9973 minus X. X. And X. Our equilibrium constant expression. Then we have our product concentrations race to the one power based on the coefficient in the balanced reaction equation divided by the concentration of our reactant to the first power. Making use of what's in our ice table. This works out to X times X over 0.9973 minus X. We're told that the equilibrium constant is 49.3. At 500 Kelvin now have, expert Is equal to 49.3 times 0.009973 -1. Which works out to 0. -49.3 x. Move everything over to the left hand side. We get X squared class 49.3 X minus 0.49169 is equal to zero. So I'll use the quadratic formula to solve this quadratic equation, which we call is given by X. Is equal to negative B plus or minus square root of B squared minus four A. C. All over two. A. And so making use of our quadratic equation then Kit X is equal to negative 49.3 plus or minus square root of 49.3 squared minus four times a. Which is one Time C which is negative 0.49169. Oliver. To a. So two times 1 extent is equal to negative 49.3 plus or minus. Working out everything under the square root of 49.3199 divided by two. So the negative value. But not make sense in this case. So you make use of positive and this works out to 0. divided by two, which works out to 0.0099715. So x 10 you go back to the ice table tells us this is the concentration of sulfur monoxide at equilibrium. It's also equal to the concentration of chloride equilibrium. Or flooring, sorry, at equilibrium. So now trying to find our moles. So our moles of sulfur monoxide take the volume 1. l Times. Then the concentration which works out to 0.0099715 moles her leader. This is 0. moles moles occurring. We're sad to be the same. So I have 1.5 L. The concentration of chlorine is the same as the sulfur monoxide, 0.01496 moles. And the moles of final chloride Is equal to 1.5 L times 0. -1, which is 0.00997, And this works out to three times 10 to the -6. Rules So we can find the total number of moles by adding up the moles of our products and reactant. So we have 0. moles plus 0. moles Plus three times 10 to the - moles. And this works out to 0.029923. Making use of the ideal gas equation. Then the total pressure people to our most total times. Gas constant times temperature divided by volume. We have 0. rolls Times are temperature of 500 Kelvin vol is 1.5 l And our our value is 0.08-0 six leaders, atmospheres per kelvin mole. So our units of Kelvin and mole cancels leaders cancels. And we left 50 units of pressure. So the total pressure is equal to 0. atmospheres. So that was part of the question that we were asked. We're asked to find the total pressure in the flask. So the total pressure in the flask verse out. 2.818 atmospheres were also asked to find the percentage of final chloride that decomposes. So if we go back to our ice table, then Excess tells us the amount of the vinyl chloride that decomposes giving our starting amount of .009973 Mueller. So you can find that percent decomposes by taking X over our initial amount of vinyl chloride, which works out to 0. Divided by 0. multiplying by 100 Percent decomposition then is 99. percent. So the percent of decomposition of the final chloride works out to 99.98%, and the total pressure, then in the flask is .818 atmospheres. Thanks for watching. Hope this helps.