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.500 g of gas collected over H,O at 29.0*C and 740.9 mm Hg occupies volume of 217.2 mL; The vapor pressure of HzO at 29.0*C is 30.0 mm Hg: What is the molar mass of...

Question

.500 g of gas collected over H,O at 29.0*C and 740.9 mm Hg occupies volume of 217.2 mL; The vapor pressure of HzO at 29.0*C is 30.0 mm Hg: What is the molar mass of the gas? PV = n Rt Answer_

.500 g of gas collected over H,O at 29.0*C and 740.9 mm Hg occupies volume of 217.2 mL; The vapor pressure of HzO at 29.0*C is 30.0 mm Hg: What is the molar mass of the gas? PV = n Rt Answer_



Answers

A 0.418 g sample of gas has a volume of $115 \mathrm{mL}$ at $66.3^{\circ} \mathrm{C}$ and $99.0 \mathrm{kPa} .$ What is the molar mass of this gas?

There is an equation which is a modification of the ideal gas law that allows you to directly solve for Moeller math. But I think from an instructive point of view, it's helpful to remember the definition of Mueller Mass as being grams of the substance over molds of the substance. The grams of the substance were given to us at 0.0.418 grams, so we could simply use the ideal gas law to solve for molds, molds being equal to P be divided by R t. The P was given to us to 99.0 killer Pascal if you choose to use the point 08 206 constant than it needs to be converted to atmospheres. If you use the other constant, it doesn't have to be. I went ahead and converted the pressure to atmospheres from Kila Pascal. And then the volume is 115 milliliters, which is 1150.115 leaders. Well, then divide by our universal gas constant 0.8 to 06 leader atmospheres per Kelvin mole and then multiply in the denominator by the Kelvin temperature. We have Celsius temperature of 66.3 so we'll add on to 73.15 Now we get four points. There are three times, 10 to the negative. Three moles. Molar mass will be the mass given to us, divided by the moles we just calculated or 104 grams per mole.

This this question 24 1 from chapter 10. And we have to solve for the molar mass off his gas. Okay, So final. And that's the castor. You're gonna be dividing that equation. No. Ive your gas law. Maybe it's equal to an arty, and they do give us the pressure of 715 films for Mercury Building. Convert that you atmosphere pressure. So we want atmospheric pressure equal to 760 millimeters of mercury. And this comes out to the point 941 atmospheric pressure. Now that we have the person, next thing we do is convert the temperature to Kelvin. No, you have 23 degrees Celsius to comfort to cover in at 200 some free. I have a temperature up 209 you know? Wow. A group. Um, no leaders born with it, you know, letters. But we're going to convert that leaders now. I can go born in 2 mL. Is it a 2.452? And this is according final Mass, because they give us a mask. So it wasn't do actually fine down city intense. Today it's brands will leaders. So from the tape, one point 00 2nd, Gramps over the point or five to waiters. And that is gonna come out with me too. I want to see Gramps. Okay, And now that we have that, we can actually stop your more mass. Now he's deriving from the ideal gas law Molar mass equal. You're dense living. That's the gas Constant five temperature overpressure. It doesn't go ahead. All this now to three grasp for a little That's the guy. Scent of 0.321 times. Yeah, Frank Richer. Just 209 Children, but with a pressure of 0.941 atmosphere and it is going to come out to be a Moeller math of 57 0.5 grands for no.

All right. So for this problem, we're looking at a particular gas and we're told a few different, uh, measurements about this gas. So we're observing this gas to be 0.418 g. Its volume is 115 mL at 66.3 degrees Celsius and 743 millimeters of mercury. So now we are asked to find the Mueller mass of this gas. And if you're not aware, the Mueller Mass is just referring to the amount of a substance, the mass of it at one mole. So this would equal grams per mole and one mole of a substance. How much of it are we seeing so to solve before Moeller Mass. We need to solve for moles because we really know the mass. So to calculate this, we just need to this one last variable. And to calculate this, it's very useful to use the ideal gas law because this will incorporate all of the different variables that we are given and leaving us to solve for the only one that we do not have. So PV this pressure times volume equals moles. Times are, which is a constant in times temperature so we can just plug these in after where we convert them into the correct units. Milliliters needs to be leaders. Degrees Celsius needs to be Kelvin and Millimeters of Mercury needs to be in atmospheres. So let's just convert to these units and then plug them into the equation. So changing from millimeters of mercury, it's atmospheres. We should know that atmosphere is equal to one atmosphere is equal to 760 millimeters of mercury. So if we write this out and ah, unit conversion sort of table, we're going to say that we want atmospheres on top. Correct. This is a good way to be consistent with your units. So one atmosphere call the 760 millimeters of Mercury, right. We want to get rid of these units, and they canceled because they're on opposite sides and they're not mysteries on top. So we need to perform this. It's a medical operation really quickly, and then we will be gifted with the answer. 7 43 fired by 7 60 is 0.98 0.982 round, which makes sense because it's a little less than one. If you look at just things in terms off How much of 7 67 43 just visually. So let's atmospheres. It's to a few others. So to convert to Calvin, we have to add 273.15 It's that simple or that complicated, depending on if you like addition or not. Okay, so we do this. I will plug this in. You could do it mentally if you are so inclined, but I like to minimize human error. When possible, We get 339.45 May 39 0.45 and then going from milliliters leaders is fairly easy. You just have to move the decimal place three places so 0.115 leaders. So now we can just rearrange the equation, solving for n and plug in everything else So n equals pressure. 0.98 0.98 times volume, which is 0.115 So very small. Ah, numerator. We will see. Now we have to divide by our anti. Right? So what is our? It is actually a constant, which is 0.82 I'll just use 0.8 and Times T, which we calculated to be 339.45 Okay, it's now we just plug these into our multiplication and divisions, and then we will get. And so let's do the denominator first. So the denominator is 27.8. You could have. Ah, nice t I calculator. You could do all this at once, but I'm just breaking it into the numerator and denominator, then 0.98 times 0.115 The new readers 0.113 when I was divide that by 27.8, which will give us a whopping zero point 004 malls. That's that's what annoyed equal when we plug everything in. So it's now calculate the molar mass. We just take our grams in the beginning and divide by the moles present at this mass. So it's 0.418 grams. Her It's per is ah, uh, term that operates as a division sign in English language. In case you didn't know, it's very useful to understand this, So this is our fraction, and we just divide So 0.418 divided by 0.4 And our answer is 104.5 grams per mole. So that is our Mueller mess. Grams per mole. Am you whatever you'd like to consider, you think?

Using the ideal gas situation, which is P. B. Equals, and Artie substituting the values directly into equation and equals 1 80 M. Pressure multiplied with zero point 75 L, divided by 0.08-1, multiplied with 373 kill win. So the number of moles will turn out to be zero 10 to fall bull. Now we need to find the Moeller mass of unknown gas. We can do it by using formula and number of moons equals, be divided by the molecular mass. The end over here is 0.0 the whole moments, and we are already provided with debate in this case, Which is 2.85 and we need to find the molecular mass solving it. The molecular mass of unknown gas will be 118.75 grams for bull.


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