At 100 °C, Kc = 4.72 for the reaction 2 NO21g2 ∆ N2O41g2. An empty 10.0-L flask is filled with 4.60 g of NO2 at 100 °C. What is the total pressure in the flask at equilibrium?

Video transcript

Hi everyone for this problem. It reads a 50 g sample of hydrogen fluoride is introduced to a three liter vessel at 350 kelvin equilibrium constant at 350 kelvin for the reaction is 2.5 times 10 to the negative to determine the total pressure in the vessel at equilibrium. So the question that we want to answer here is the total pressure in the vessel at equilibrium. Since we want to find equilibrium pressure, what we're going to need to do is construct an ice table for the reaction. So let's first start off by writing out our reaction and creating an ice table for it. Okay, so we have our reaction and we're going to write ice for the initial concentration change in concentration and equilibrium. Alright, so what we're going to need to do is we're going to need to find the initial concentration of hydrogen fluoride. That initial concentration is going to go here, but we don't know what it is. So we need to solve for it. We do know that we have a 50 g sample and we can use the molar mass of hydrogen fluoride to solve for to go from grams to moles. Okay, so we have 50 g of hydrogen fluoride and we want to go from grams to moles. So we need the molar mass in one mole of hydrogen fluoride. There is 20. g of hydrogen fluoride. So our units for grams of hydrogen fluoride cancel. And we're left with moles of hydrogen fluoride. And when we do this, what we get is 2. moles of hydrogen fluoride. Okay. And we want initial concentration because that's what the iro of our equilibrium Table needs remember concentration is moles over leader. Okay. So we want the concentration of hydrogen fluoride and we need moles over leader. We just solve for moles and we know that we have 2.2.4988 moles. And the volume was given in the problem, it is three leaders. So this is going to be over three leaders. So when we saw for the concentration Of hydrogen fluoride, what we get is 0. Molar. Now this is the number we're going to put for our initial concentration row of the ice table. Okay. And we have no products. So that means our reaction is going to shift in the forward direction where our concentration of reactant is going to decrease and concentration of products is going to increase. So for the c row of our table which represents change in concentration for our reactant we have a minus and we need to take a look at our stoke eom a tree here we have two moles. So it's going to be minus two X. And for our products because our products concentration is increasing it's going to be positive and we only have one mole of each. So both of these become just plus X. So now we can combine both rows of our ice table. So 0.8329 minus two X. And then this is X. And this is X. Alright, so now that we've constructed our ice table, we can go ahead. I'm gonna move this over here. So we have enough space. Okay, so now we can go ahead and right out our equilibrium constant expression. Okay, and that is K. C. Is equal to our equilibrium constant, is equal to the concentration of products. Mhm. Over the concentration of reactant. And in this case we're looking at pressure. Okay, so looking at our balanced equation, what this comes out to in terms of an equation, it's going to equal the concentration of hydrogen gas, times the concentration of chlorine gas over concentration of hydrogen fluoride. And for our equation we have two moles of this hydrogen fluoride, so that two moles now becomes an exponent. Alright, so now what we need to do is we need to plug in the equilibrium row of our ice table into this equilibrium constant expression. And we also need to plug in the value of K. C. Okay, so we know what the value of K. C. Is. It was given in the problem K C is equal to 2.50 times 10 to the negative two. And this is going to equal we're gonna plug in everything into our ice table here for the concentration of products over concentration of reactant. So we're going to get equal to X times the concentration of X over the concentration of 0.8329 minus two X. Okay. And so if we simplify this, this becomes 2.50 times 10 to the negative two is equal to X squared over. And this there should be a squared right there. Okay, so make sure we put that there because we need to pay attention to the stoke eom a tree. Okay, so this becomes 0.8329 minus two X squared. Okay, so because we have a square on both sides on the right side of our equation, we can apply the perfect square method. So we're gonna take a square, we're gonna take the square root of both sides And this is gonna be us applying the square root method. So when we do this, what this now becomes is 0. that should be in the same color. So this becomes 0.1581. So that's the square root of the left side. And we're taking the square root of the right side. And when we do that, that's gonna make the squares drop. So that's just gonna leave this as X over 0. minus two X. Okay, so now we're going to simplify by getting rid of this fraction. Okay, so when we simplify and get rid of the fraction what we get is 0. minus 0.3162 X equals X. We want to yep. And this is going to give us our X. So let's write it the other way around. When we simplify this, what this becomes is when she races this so this becomes X equals The following. And this gives us a final value of x equal to zero 1000 molar. Alright so if we go back to the equilibrium role of our ice table now we're going to plug this value of X. N. And solve for our concentrations of hydrogen gas flooring gas and hydro Hydrofluoric acid. Okay. And or not Hydrofluoric acid. Excuse me, hydrogen fluoride. Okay so when we do that, what we're going to get is the concentration of hydrogen gas at equilibrium is equal. Both this and the concentration of flooring gas are the same because they're both X. Okay So their concentration that equilibrium is 0.1000 moller. And the concentration for hydrogen fluoride at equilibrium is equal to zero 8329 -2X. So we need to plug in the value of x here. So we get 0.8329 - times X. Which is 0.1000. And this gives us a value of 0. moller. Okay so our concentration of hydrogen fluoride at equilibrium is 0.6329 moller. Alright, so let's just highlight that so that we can recall this is our concentration for hydrogen gas and flooring gas and then hydrogen fluoride. Alright, so but we're not done. The question asks us to calculate the total pressure, but before we can calculate the total pressure, let's determine the total number of moles in the vessel at equilibrium. So we're going to take the sum of all of the molds we just solve for and we're going to multiply it by the volume of the vessel. Okay, so we're going to so we're going to find and total and that is going to equal the sum. So this is going to equal the sum of hydrogen fluoride at equilibrium plus hydrogen gas at equilibrium plus flooring gas at equilibrium. And this is gonna be multiplied by the volume of the vessel. So let's go ahead and solve for that. Okay, so we're going to have 0.6329 moller plus 0.100 moller plus 0.1000 molar. And the volume of the vessel is three liters. Okay, So our total number of moles is equal to 2.4987 moles. And now we can solve for the total pressure. Okay, and for us to solve for the total pressure, the total pressure is equal to the total number of moles times gas constant r times temperature over volume. Okay, so let's go ahead and plug in. Those values are the total number of moles we just solved for which is 2.4987 times gas constant R which is 0. leaders. Atmosphere over mole kelvin. And this is multiplied by the temperature Which is 350 Kelvin and this is all over the volume, which is three leaders. Okay, so once we do this calculation will solve for the total pressure and the value that we're going to get is 23.9 atmospheres and this is going to be our final answer. That is it for this problem. I hope this was helpful.