At 100°C, the equilibrium constant for the reaction COCl₂(𝑔) ⇌ CO(𝑔) + Cl₂(𝑔) has the value 𝐾_𝑐 = 2.19×10⁻¹⁰. Are the following mixtures of COCl₂, CO, and Cl₂ at 100°C at equilibrium? If not, indicate the direction that the reaction must proceed to achieve equilibrium. (a) [COCl₂] = 2.00×10⁻³ 𝑀, [CO] = 3.3×10⁻⁶ 𝑀, [Cl₂] = 6.62×10⁻⁶𝑀

Video transcript

hi everyone for this problem. It reads the following reaction has an equilibrium constant of 0.953 at 125 degrees Celsius we have hydrazine, yields nitrogen gas plus hydrogen gas at 100 and 25 degrees Celsius. The following concentrations were mixed in a flask. Will the mixture reach equilibrium? If not in which direction should the reaction proceed to reach equilibrium? So what we're trying to answer here is will the mixture reach equilibrium. An important piece of information we're given in this problem is the equilibrium constant. Okay, that 0.953. In order for us to know if this mixture will reach equilibrium, we need to know what our value for our reaction quotient, which is Q. What is that value? By comparing K. R equilibrium constant to Q. Our reaction quotient will be able to determine in which direction our reaction will proceed to establish equilibrium. So with those two values K and Q. When K is greater than Q. Our reaction is going to prefer or favor the four direction. Okay, so the four direction is preferred or favored when K is greater than Q. However, when K is less than Q, the reverse direction is favored. When K is equal to Q, then the mixture or the reaction is at equilibrium. Okay, so the question that we want to answer is will the mixture reach equilibrium? So the way we'll know if it will reach equilibrium is if we if K is equal to Q, we already know what K is K is equal to 0.953. That was given in the problem and K are equilibrium constant. Has an expression which is the concentration of our products raised to its Tokyo metric coefficient over the concentration of our reactant. Okay, so this is what our equilibrium expression is. So because that's what K represents, our equilibrium concentrations however Q. Which we don't know what this value is, it has the same expression except the values are non equilibrium values. Okay, so the values were given in the problem are are non equilibrium values. So these values are going to go into our expression for Q. So that we can solve for the value of Q. Okay, so let's go ahead and do that. So we're going to get Q and we're just going to plug in here. So for nitrogen gas our value is 4.50 times 10 to the negative five Moeller. Okay, for hydrogen gas our value is 3.50 times 10 to the negative five molar. And remember this is squared because we're raising it to its Tokyo metric coefficient. So because we have two moles of hydrogen gas, we're going to raise that to and make it an exponent over our concentration of reactant. Okay, so now that we've plugged this in we can solve so we can get a value for Q. And when we do we get Q is equal to 1.8375 times to the negative 11. So we know what K is. We know K is equal to 110.953 and we know Q is 1.8375 times 10 to the negative 11. So here we can see that K is greater than Q. Okay, so we'll write that here, K is greater than Q. So to answer the question, will the mixture reach equilibrium? The answer is going to be no. And it asks if not in which direction should the reaction proceed to reach equilibrium? So in order for us to reach equilibrium because K is greater than Q, that means the four direction is favored. So that means we're going to need to proceed to the right Or in other words in the four direction. Okay, two reach equilibrium. So that is going to be the final answer to this problem. This part here that we're highlighting So, no, the mixture is not an equilibrium because K does not equal Q K is greater than Q. So we're going to proceed to the right or in the forward direction to establish equilibrium. Okay, so that's it for this problem. I hope this was helpful