Consider the reaction: 2 Ag2O(s)¡4 Ag(s) + O2( g) If this reaction produces 15.8 g of Ag(s), what total volume of gas can be collected over water at a temperature of 25 °C and a total pressure of 752 mmHg?

Video transcript

hi everyone for this problem, we're told to consider the reaction of 5.693 g of N A two s. Following the balanced equation below The total pressure of the gas is 121.2 killer Pascal's calculate the volume of H two s. That is collected over water at 25 degrees Celsius. The vapor pressure of water at 25 degrees Celsius is 0.313 A. T. M's. Okay, So we're going to need the ideal gas law in order to solve this problem. And that law tells us that P. V. Is equal to N. R. T. And for this problem specifically, we're being asked to calculate volume. So we need to rearrange this equation so that it solves for volume. And so we can do that by dividing both sides of our equation by P. And so that leaves us with volume is equal to N. R. T over P. So that's going to be the equation we need so let's go ahead and plug in what we know and solve for anything that's missing. So we know N. Is equal to moles. So we need moles of N A two S. But were not given that were given grams. And so we need to go from grams to moles. So let's do that first. So most of and A To S. So we're told we have 5. g of N.A.. To S. And so using the molar mass we can go from moles, we can go from grams to moles. So in one mole of NA two s. Using our periodic table and the molecular weights we can see that it's the molar mass is 78. g of N A two S. And so here we see that our grams cancel and we're left with moles. And so we have 0. 29 moles of and a to us. Okay, perfect. So we have our moles are is our universal gas constant. So we can, I'm going to plug in as we solve. So our volume is equal to N we said and is equal to 0. 29 most. Our is our gas constant. And this is a value we should know it's not going to be given. And that value is 0. Leaders times atmosphere over moles. Time kelvin. Okay. And temperature were given a temperature of 25°C. But if we look at our gas constant, our temperature is in kelvin. So we need to convert this temperature from Celsius to kelvin. And so all right here two is our temperature. So we have 25°C. And to go from C to Kelvin will add 273.15. So we get our temperature in Kelvin is 298.15 Kelvin. So we can now plug that in. So we have 298. Okay, so the last thing we need is P. R. Pressure. And in order to find our pressure, our pressure Of H two s. Is going to equal our total pressure. So p total minus our pressure of water. Okay Because we're calculating the volume of H. two s. And so we're given a pressure were given the total pressure. And the problem they tell us the total pressure is 121 point to kill a pascal's but we need to convert this to A. T. M. So our p total is equal to 1:21.1 killer pascal's. We need to convert this to A. T. M. So in one killer pascal There is to the 3rd Pascal's. And in one a. t. m. There is one There's 10, or 101, 325 pascal's. Okay so this gives us a total pressure of one point me move things over a little bit. I'm gonna make I'm gonna make this smaller. Okay so one point 196 A. T. M. Is our total pressure. Okay? And they tell us that the vapor pressure of water is 0.313 A. T. M. And so to find the pressure of H two S. We're going to take the total pressure minus the pressure of our vapor to get the final pressure to plug into our problem. And so that gives us our pressure of H. Two S. Is equal to our total pressure. As I said before is 1.196 a t. M minus the Vapor pressure of our water 0.03 13. That gives us 1. a t. M. And that's going to be what we plug in. So we have Over 1.1658 T. M. Okay, so now we have everything that we need to solve for our volume. So once we plug everything in we get a volume of 1.531 l and this is our final answer. This is the volume of H to us that is collected. Okay, that's the end of this problem. I hope this was helpful.