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7. Gases

Under certain conditions of pressure and temperature, the **Ideal Gas Law** can determine the **density **of a gas.

The Ideal Gas Law (Density)

1

concept

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we're calling. That density represents the amount off mass per unit of volume. And when it comes to our density formula, its density equals mass over volume. Now, gasses are much less dense than solids and liquids. So when it comes to their density, we're gonna say their density is in grams per leader. I am here. It's still mass of the gas and grams, and then here Volume V will be in leaders. So again, when it comes to density, it's mouse over volume and gas is being much less dense. Don't use grams per milliliter or grams per centimeters cube, but instead use grams per liter.

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example

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here. It says an unknown gas sample has a density of 1.70 g per leader. If if the sample has a volume of 120 miles, what is its mass in grams? Alright, so here were given to values. But we want to start out with 120 miles because it just has one unit by itself, easier to manipulate. So we're gonna start out with 1 20 millimeters, realize that we need to isolate our grams, which are found here. And in order to isolate those grams, I need to cancel out the leaders. So that tells me that I need to convert 120 m Els into leaders first. So remember, one Millie is 10 to the negative three leaders. Now that I have leaders, I can bring in my density, which is 1.7 g per one leader. So here leaders cancel out, I'll be left with grams at the end. When I punched that in, that gives me 0.204 g off my unknown gas. Here, my number has three sig figs because 1.70 has three sig figs and this has four Sig figs. Remember, we want to go with the least number off Sig Figs when? When it's reasonable. Here, 40.204 g is a reasonable answer for unknown gas.

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Now we can say that the ideal gas law can be used to determine the density of a gas under certain pressure and temperature conditions. Here, we're going to say that the new derived version of the ideal gas law, which we can apply to density, is d equals P times em over r t. And to help us remember this order chest, remember, dreams push me over rough times here Dreams D Stands for density. Push me is pressure times molar mass over our times team rough times. So if you could remember this phrase, it's a great way to remember this version of the ideal gas law when it relates to density. Now, if you wanna look and see how we derive this formula, you can click on to the next video, but only do so if you're a professor. Really cares on how you derive these different types of formula. If they don't, they just remember this phrase. After that, go to the next series of videos and let's put this formula to practice

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So if you clicked on this video, that means you want to see how we derive this new version of the ideal gas law. So it all begins with our density formula. Remember, density equals M over V. Remembering this, we move on to the ideal gas law where we're dealing with Mueller Mass. Remember, Moeller Mass equals Marty over PV, and we just said that M over V represents density. So take them out and put in density. We still have our tea and overpay. We need to isolate density. So just use algebra to isolate it. Multiply both sides by pressure. So Moeller mass times pressure equals d rt. Isolate our density by dividing up Artie and we see now that density equals p times em over r t So that's how we went about an isolated and derived this new formula for density. Now this is how we derived it. But just remember, dreams push me over rough times, knowing that helps you to write the formula very quickly. Now that we've seen this formula, click on to the next video and let's put it to work

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example

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here we're told that a gaseous compound of nitrogen and hydrogen is found to have a density of 0.977 g per leader at 0.69474 atmospheres and 3 73.15 kelvin. What is the molecular formula of the compound? We'll realize here in this question they're giving us density. They're giving us pressure and they're giving us temperature. With this information, I could find the more mass of this unknown gas. So here we're going to say that dreams push me over rough times and we're going to say that we have density. We have pressure, we have temperature. And we always know what our is. We just need toe isolate our Mueller Mass. So multiply both sides by rt. So are our tee times d equals p times Mueller Mass divide both sides by pressure. So Mueller mass equals d r t overpay. We'll take the information given to us. Our density is 0.977 g per leader. Our is our gas constant temperatures already in Kelvin and pressure is already in atmospheres. Doing this will see that we isolate So Adam atmospheres air gone. Kelvin's air gone leaders are gone, we'll have grams per mole. So we plug this into our formula. We're going to get here as our mass 06 g per mole. So here's our Moeller Mass. All we do now is we look at the different compounds and we would just calculate their Mueller masses and see which one comes closest to this 43.6 g per mole. Now, if you did this correctly, you would see that the answer would have to be Option C. It's the one with the mass closest to our answer. It has a Mueller Mass. Approximately equal to 43.38 g per mole. So option C would be the answer for this particular question. So realize they're giving us density, pressure and temperature. That means we can use the density form of the ideal gas law to help us find Moeller Mass and then use that information to compare to the molar masses off all these gasses

6

Problem

Consider two containers of gases at the same temperature. One has helium at a pressure of 1.00 atm. The other contains carbon dioxide with the same density as the helium gas. What is the pressure of the carbon dioxide gas sample?

A

0.063 atm

B

0.091 atm

C

0.133 atm

D

1.51 atm

E

2.71 atm

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Problem

Determine the molecular formula of a gaseous compound that is 49.48% carbon, 5.19% hydrogen, 28.85% nitrogen, and 16.48% oxygen. At 27°C, the density of the gas is 1.5535 g/L and it exerts a pressure of 0.092 atm.

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Additional resources for The Ideal Gas Law: Density

PRACTICE PROBLEMS AND ACTIVITIES (18)

- Consider the following samples of gases: If the three samples are all at the same temperature, rank them with...
- A 1.0-L container of liquid nitrogen is kept in a closet measuring 1.0 m by 1.0 m by 2.0 m. Assuming that the ...
- Rank the following gases from least dense to most dense at 101.33 kPa and 298 K: O2, Ar, NH3, HCl.
- Rank the following gases and vapors from least dense to most dense at 101.33 kPa and 298 K: water vapor 1H2O1g...
- (a) Calculate the density of dinitrogen tetroxide gas 1N2O42 at 111.5 kPa and 0 °C.
- (b) Calculate the molar mass of a vapor that has a density of 7.135 g>L at 12 °C and 99.06 kPa.
- What is the density (in g/L) of hydrogen gas at 20.0 °C and a pressure of 1655 psi?
- The matter in interstellar space consists almost entirely of hydrogen atoms at a temperature of 100 K and a de...
- A sample of N2O gas has a density of 2.85 g/L at 298 K. What is the pressure of the gas (in mmHg)?
- What is the density in g/L of a gas mixture that contains 27.0% F2 and 73.0% He by volume at 714 mm Hg and 27...
- What are the molecular weights of the gases with the following densities: (b) 1.053 g/L at 25 °C and 752 mm Hg
- Propane, C3H8, liquefies under modest pressure, allowing a large amount to be stored in a container. (a) Calcu...
- Two 112-L tanks are filled with gas at 330 K. One contains 5.00 mol of Kr, and the other contains 5.00 mol of...
- The density of a gas of unknown molar mass was measured as a function of pressure at 0 C, as in the table that...
- The density of a gas of unknown molar mass was measured as a function of pressure at 0 C, as in the table that...
- An 11.5-mL sample of liquid butane (density = 0.573 g>mL) is evaporated in an otherwise empty container at ...
- A quantity of N2 occupies a volume of 1.0 L at 300 K and 1.0 atm. The gas expands to a volume of 3.0 L as the ...
- A gas mixture composed of helium and argon has a density of 0.670 g>L at a 755 mmHg and 298 K. What is the ...

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