Gaseous compound Q contains only xenon and oxygen. When 0.100 g of Q is placed in a 50.0-mL steel vessel at 0 °C the pressure is 0.229 atm. (a) What is the molar mass of Q, and what is a likely formula?

Video transcript

Hi everyone. This problem reads gas A is composed of nitrogen and oxygen at 20 degrees Celsius a 200.230 g sample of a exerts a pressure of 1.844 atmospheres while in a 100 mL container determine the molar mass and probable formula of gas A. So we have two things we need to answer for this problem. The first is the molar mass and the second is the probable formula of gas A. For us to determine the molar mass. The equation that we're going to need is molar mass is going to equal mass times the gas constant. R times temperature Over pressure times volume. Okay, so let's go ahead and plug in what we know based off of what is given in the problem. So molar mass is equal to mass in the problem. We're told the mass of the sample is .230 g. So we'll go ahead and plug that in for the mass. 0.230g are is a gas constant and that constant is 0.08206. Leaders atmosphere over Mole Kelvin and T is temperature. So we're given the temperature is 200. Excuse me, 20°C. But we need but we need this temperature in Kelvin because if we look at our units for our constant, it's moles per kelvin. So our temperature unit is kelvin. So we're going to add 273 to convert that degree Celsius to kelvin and this is all over pressure times volume. Okay, the pressure were given in the problem. It's 1.844 atmospheres and the volume. We're given it in milliliters. But if we look at our gas constant R R unit for volume is in leaders. So we're going to take 100 mL and convert this to leaders. And the conversion is and one millimeter there is 10 to the negative three leaders. Okay, so our volume is 0.100 liters. So let's go ahead and plug that in. So we just plugged everything in. So we're going to get our molar mass is equal to 30.5 g per mole. So that's part one of our problem. So go ahead and write our molar mass is equal to 30.5 g per mole. And we can highlight that as our final answer for the molar mass. The second part of this question asks us for a probable formula for gas A So for this formula, we're going to need the molar masses for both of our gasses. So let's go ahead and write those down. The molar mass for nitrogen is .0067 g per mole. And the molar mass of oxygen Is 15. g per mole. So what we're going to do here is we just calculated the molar mass. So we're going to take the molar mass that we just calculated so that 30.5 g per mole. And we're going to subtract Our mass of nitrogen from it, our lowest mass. So that is 14. 67 g per mole. When we do that calculation, we get 15. g per mole. Alright, so the number of oxygen's is going to equal the grams that we just calculated. So that 15.9983. And we're going to divide it by the molar mass of oxygen 15.999. So when we do that calculation, we get 0.9996, which we can round 21. Alright, so that means we have one oxygen. Alright, so our formula, our probable formula is going to be an O. So we calculated our molar mass and we calculated our probable formula. That is it for this problem? This should read number of oxygen right there. Okay, so that is it for this problem. I hope this was helpful