Helium gas with a volume of 3.20 L, under a pressure of 0.180 atm and at 41.0°C, is warmed until both pressure and volume are doubled. (b) How many grams of helium are there? The molar mass of helium is 4.00 g/mol.

Video transcript

Hey everyone in this problem. We have an ideal carbon monoxide gas that initially has a temperature of 290 Calvin in a pressure of three atmospheres. The gas undergoes an expansion from 0.5 m cubed to one m cubed. The final pressure is four atmospheres and carbon monoxide molar mass is 28 g per mole. Were asked what is the mass of ceo? All right. So we're asked for the mass. Were given the molar mass. Let's recall that we have the following relationship. We have end. The number of moles is equal to the mass M divided by the molar mass. Big end. Okay, We want to find the mass. Little m We know the molar mass began but we don't know the number of moles. Okay, so let's try to find a way to figure out what N is. So we can put it into this equation and find em Okay, now let's recall. We have an ideal gas, we can use the ideal gas law and the ideal gas law tells us that PV is equal to N. R. T. Okay, so the pressure, the volume, the number of moles in the gas constant R in the temperature. T. Okay, so this gives us a way to find that value of N. Alright, let's write out the information we know. Okay, well, let's start with P We need to find P for equations. So let's do P one. Okay, so the initial pressure we're given is three atmospheres And this is gonna be equal to three times 1.013 times 10 to the five Pascal's Which is gonna give us three 0. times 10 to the five pascal's. Okay so we just wanted to convert our atmospheres into pascal's. Okay so that's the pressure. What about the volume? The initial volume V one. We're told that it expands from 0.5 m cubed. So our initial volume is going to be 0.5 m cubed. And our initial temperature T one We're told is 290 Kelvin. We know are the gas constant. Okay? We have P. V. And T. This is gonna let us find end. So let's plug in our values. It's all for end. We get 3.39 times 10 to the five pascal's Times of volume, 0.5 m cubed is equal to end. The number of moles Are the gas constant. 8. jewels per more Calvin Times the temperature. 290 Calvin. Alright so the unit of Calvin is going to cancel here. We're gonna divide by jewel per mole. Okay? We have pascal meters cubed divided by jewel per mole. The unit that's gonna be left is going to be just A mole. Okay so let's see that on the left hand side simplifying. We get 1.5195 times 10 to the five jewels. On the right hand side we have n times 2411. joules per mole. Okay. on the left hand side we have pascal meters cubed, which gives us jules. Okay so when we divide again, the unit we're left with is mole. We get N. Is equal to 63.0 to 2073 mol. Now remember what we're finding. Okay, we found the number of moles but we want to find the mass M. So we can go back to the equation we had previously where N. Is equal to little M. Over big M. And substitute the new information 63. 073 is equal to little M. Over big M. The molar mass which is 28 g. Her more. Okay. And appear our unit should be more. And if we multiply we get the mass m. The unit of mole and Permal will be will cancel. And we're left with the unit of Graham. We get 1,764. g for the mass of C. 0 1764.6 g. And if we round that to the nearest gram, we're going to have the answer. D Okay. The mass is 1765 g. Thanks everyone for watching. I hope that video helped see you in the next one