A sample of nitrosyl bromide (NOBr) decomposes according to the equation 2 NOBr(𝑔) ⇌ 2 NO(𝑔) + Br₂(𝑔) An equilibrium mixture in a 5.00-L vessel at 100°C contains 3.22 g of NOBr, 3.08 g of NO, and 4.19 g of Br₂. (b) What is the total pressure exerted by the mixture of gases?

Video transcript

hi everyone for this problem we're told to consider the reaction below an equilibrium mixture of 38.9 g of c 25 g of H 2026.9 g of C 02 and 1.23 g of H two is kept in a two liter container at 1260 kelvin, calculate the total pressure of the mixture. Okay, so our goal here is to calculate the total pressure. What we can use to solve this problem is the ideal gas law which is pressure times volume is equal to N. R. T. Where N is our number of moles are is our gas constant and T. Is our temperature. So we want to calculate pressure. So we need to isolate pressure in this ideal gas law and we can do that by dividing both sides of our equation by volume. Okay, so when we do that, we get pressure is equal to N. R. T over volume. So let's take a look at what we already know and figure out what we're missing. So N is equal to moles. What were given in the problem is grams. We don't have moles. So we're going to need to find the moles of everything in our reaction. So we don't have that. Our represents our gas constant, which we know is 0.08-0 six leaders time atmosphere over Mole Times Kelvin. This is a value. We should have memorized temperature is represented by T and they give this to us. It is 12 60 kelvin and our volume was also given at two leaders. So all we need to solve for in order to solve for our pressure is we need to figure out our total number of moles. Okay, so we're going to find out our total number of moles for everything on our reaction. So let's go ahead and start with our moles of C. O. Okay, so we know we have 38.9 g of C. 02. Go from grams to moles. We need molar mass. So in one mole of C. O. We have using our periodic table 28. g of C. O. So taking a look at our units here are grams cancel. And we're left with moles our final moles for C. O. Is going to be 1.39 moles of C. O. Okay, so number two is our moles of H 20. We're told we have 20 five g of H 20. We need to go from grams to moles and we can do that using the molar mass. So one mole of H 20. Is 18.02 g of H 20. Our grams of H 20 cancel. And we're left with a moles of 1.39 moles of H 3rd. We have our C 02. So For moles of CO We're told we have 26. g of CO2 to go from grams to moles. We use the molar mass. So one mole of C 02 is 44.1 g of C 02. Okay, Our g of CO2 cancel. And we have 0.61 Moles of CO two. Lastly we have Moles of H two. So we're told we have 1. g of H two to go from grams to moles. We use the molar mass and molar mass is 2. g of H two. So our grams cancel and we're left with moles. So our final answer is 0.61 moles of H two. So because we're calculating the total pressure, we need to add all these values up to get total moles. So let's go ahead and do that. When we add up all of these values, we're going to get total moles Is equal to four. Okay, so now that we know are total moles. We can plug that into our ideal gas law equation to solve for our total pressure. So let's go ahead and do that. So we said pressure is equal to N R. T over V. So our pressure is going to equal And we just calculated is four moles R is 0.08206 leaders. Times atmosphere over more Times Kelvin and our temperature is 12, 60 kelvin and this is all over our volume of two leaders. So we need to make sure everything cancels here. The unit that we want for pressure is A. T. M. So let's see our moles cancel. Our leaders cancel and our kelvin cancels. So we're left with a. T. M. Which is what we want for pressure. So our final pressure is going to equal 206.8 A. T. M. Okay. And that is going to be our final answer. Our total pressure of the mixture is 206. TM. That's the end of this problem. I hope this was helpful.