In order to accurately study the effect that changes in pressure, temperature and moles have on volume, chemists will often run their experiments under **Standard State conditions**.

**Concept:** Understanding Standard State Conditions

Welcome back, guys! In this new video, we're going to take a look to see what happens to our gas behavior under standard states. We're going to say sometimes chemists want to understand the influences that pressure, volume or temperature have on a particular gas particle. To do this, they do these experiments under what we call standard conditions.

We're going to say that these standard conditions are sometimes referred to as STP. STP just means standard temperature and pressure. We're going to say standard temperature is zero degrees Celsius. which really is 273.15 Kelvin. Standard pressure is one atmosphere.

**Concept:** Standard Molar Volume

We're going to say under standard state conditions, the volume of one mole of any gas, an ideal gas just means a gas that behaves as though it's by itself. One mole of any gas under STP will then have the same volume. At STP, one mole of carbon dioxide, one mole of nitrogen gas, or one mole of helium gas – all of these gases look different. Some of them are just atoms by themselves. Others are different elements connected together.

Under standard state conditions, under STP, all moles of gases have the same volume. They all have 22.4 liters. We're going to say that this volume is known as our standard molar volume. Remember, under STP conditions, one mole of any type of gas will have that as their volume.

At **STP**, **1 mole** of any ideal gas will occupy exactly **22.4 Liters** of volume inside a container.

Knowing the meaning of STP allows you to now further manipulate the Ideal Gas Law.

**Concept:** Combined Gas Law

Let's look at this example which uses our STP concept. We're going to see a sample of Freon-12 occupies 20.7 liters at 25 degrees Celsius and 947 torrs. Now they're saying what is the volume under standard conditions. Remember, what are they asking me? They're asking me to find the volume. But here they already gave me a volume. This must be my volume 1 and this must be my volume 2. They also gave me a temperature and they gave me a pressure. Here, they’re saying under standard conditions. Standard condition means we have a standard pressure and a standard temperature.

Our P2 would be one 1 atmosphere and our standard temperature would be to 273.15 Kelvin. Since we’re deal with a gas, we write PV equals nRT. Again guys, we're dealing with two sets of data. Remember, what have we done when we have two sets of something, two volumes or two pressures? We’d have to check to see who they're talking about. They're talking about pressure, they’re talking about volume and they're talking about temperature. They're not talking about moles because moles are being held constant, so we ignore it. R is our constant as well so we ignore that too. Everything is not on the same side of the equation sign. Divide everything by T to bring it over to the left. PV over T, since we’re dealing with two sets of data, it’s P1V1 over T1 equals P2V2 over T2.

This creates a whole new type of gas law, which we call the combined gas law. We haven't seen that until now. This is our combined gas law P1V1 over T1 equals P2V2 over T2. This is our combined gas law. We're going to plug in the units that we know into this combined gas law. But first, you have to change the temperature into Kelvin and you have to change those 947 torrs into atmospheres. T1 is 25 degrees Celsius, so all we have to do is add 273.15 which gives us 298.15 Kelvin. Pressure 1 is 947 torrs. We just have to change this to atmospheres. For every 1 atmosphere it's 760 torrs. When we do that, we get our answer as 1.24605 atmospheres. All we have to do now is plug it in and solve for our missing variable. Our P1 is 1.24605 atmospheres. Our volume 1 I told you was 20.7 liters. Our temperature 1 was 298.15

Kelvin, equals.

The pressure 2 was 1 atmosphere. That's really not going to change anything, so we plug it in anyways, 1 atmospheres. V2 is what we're looking for over temperature 2 which is 273.15 Kelvin. What we're going to do here is we’re just going to solve for everything on the left. Do the P1 times the V1 divided by T1. When we do all of that, the left side gives me 0.086511 liters times atmospheres over K. This still equals my 1 atmosphere times V2 divided by 273.15 Kelvin. Multiply both sides now by the 273.15 Kelvin. Kelvins cancel out, so then that’s going to give me 23.6305 liters times atmospheres still equals 1 atmosphere times V2. Divide both sides by the 1 atmosphere, which doesn't do anything. All it does is it helps get rid of these atmospheres in the units. So then V2 equals, we're going to just do 3 sig figs here. It's 23.6 liters. That would be the answer for our volume 2.

Again guys, remember even though we started out with the ideal gas law, because we have two sets of data again, we have to manipulate the ideal gas law. Doing that helped us isolate our answer here for V2. Now that you’ve seen this and now that you understand what STP is, I want you guys to attempt the next question.

**Concept:** Using the Ideal Gas Law to find density or molar mass

We're going to say that we're used to seeing the ideal gas law as PV equals nRT. But we should realize that we can manipulate this equation further in order to find the molar mass of the gas, or the density of a gas. Here, to find the molar mass of a gas, we change it. This capital M is not molarity, it's molar mass. Remember, the units for molar mass or molecular mass are grams per mole. We’re going to say the molar mass of a gas is equal to mRT over PV. We're going to say m represents the mass of the gas in grams, and then all the other variables stay the same. R is still our gas constant. Temperature is still in Kelvin. P is still in atmospheres and volume is still in liters.

If we want to find the density of a gas, we could say the density of a gas is equal to pressure times the molar mass divided by RT. This can become our equation. We could also further manipulate if we wanted the second equation. We could have combined mass and volume together to give us one thing. Remember, mass over volume helps us find density. We could have manipulated this further by saying molar mass of a gas is equal to density times RT over P. We could have used this as well. But then again, if we have a question dealing with the density of a gas, we know we could use this one and we could just manipulate it.

Even though this is a potential equation, we can get to it by just manipulating this third one. I’d recommend just remembering these three. If you're dealing with a question that gives you density and wants the molecular weight, you just use the third one. Manipulate it to find your answer.

The Ideal Gas Law can be further manipulated into new equations. These new equations can help us find the density or molar mass of a gas.

When calculating the density of a gas it is essentially to also recall the formula of that gas in order to find the molar mass, M.

Remember that units for molar mass are grams of compound divided by the moles of that compound.

**Problem:** An unknown gas sample weighs 3.12 g. If it has a volume of 0.206 µL when the temperature is 45^{o}C and the pressure is 957 torr. What is its molar mass?

A sample of carbon dioxide gas (CO_{2}) has a volume of 2.5 L at standard temperature and pressure (STP).

How many molecules of carbon dioxide gas are in the sample?

Watch Solution

If the density of an ideal gas at STP if found to be 0.716 g/L, what is its molar mass?

Watch Solution

Be sure to answer all parts.

How many moles of gaseous arsine (AsH_{3}) occupy 0.273 L at STP?

What is the density of gaseous arsine?

Watch Solution

Enter your answer in the provided box.

A sample of Freon-12(CF_{2}Cl_{2}) occupies 10.0 L at 293 K and 128.00 kPa. Find its volume at STP.

Watch Solution

A sample of oxygen gas has a volume of 2.50 L at STP. How many grams of O_{2} are present?

Watch Solution

An open flask sitting in a lab fridge looks empty, but we know that actually it is filled with a mixture of gases called air. If the flask volume is 1.50L, and the air is at standard temperature and pressure, how many gaseous molecules does the flask contain?

Watch Solution

Calculate the volume occupied by 56.5 g of argon gas at STP.

22.4 L 31.7 L 34.6 L 1, 270 L 1, 380 L

Watch Solution

Calculate the volume of 63.5 g of carbon monoxide at STP. Report your answer to one decimal place!

Watch Solution

Find out the volume contained by 6.8 g of ammonia at STP. (N=14, H=1)

Watch Solution

Arrange the following gases in order of decreasing density at STP. Rank from largest to smallest.

F_{2}

O_{2}

Cl_{2}

Ne

Watch Solution

Use the molar volume of a gas at STP to calculate the density (in g/L) of oxygen gas at STP.

Watch Solution

Which gas sample has the greatest volume at STP?

a. 20g of Ne

b. 2g of H_{2}

c. 8g of He

d. 20 g of N_{2}

Watch Solution

Which of the following gases has the largest density at STP?

a. He

b. C_{2}H_{2 }

c. F_{2}

d. N_{2}

e. H_{2}

Watch Solution

Which of the following samples will have the greatest volume at STP?

a. 22 g Ne

b. 22 g He

c. 22 g O_{2}

d. 22 g Cl_{2 }

e. All have the same V at STP

Watch Solution

When aluminum is placed in concentrated hydrochloric acid, hydrogen gas is produced.

What volume of H_{2}(g) is produced when 6.2g of Al(s) reacts at STP?

Watch Solution

One mole of nitrogen and one mole of neon are combined in a closed container at STP.

How big is the container?

Watch Solution

Consider three 1-L flasks at STP. Flask A contains NH _{3} gas, flask B contains NO_{2} gas, and flask C contains N_{2} gas. In which flask are the molecules least polar and therefore most ideal in behavior?

Watch Solution

Methane, CH_{4}(g), reacts with steam to give synthesis gas, a mixture of carbon monoxide and hydrogen.

CH_{4} (g) + H_{2}O(g) → CO(g) + H_{2}(g) [unbalanced]

What mass of hydrogen is formed if 275 L of methane (measured at STP) is converted to synthesis gas?

Watch Solution

Consider the following gas phase reaction:

2NO(g) + O_{2}(g) → 2NO_{2}(g)

400. mL of NO at STP is reacted with 500. mL of O_{2} at STP. Calculate the volume of the reaction mixture at STP after the reaction goes to completion.

a. 700 mL

b. 800 mL

c. 900 mL

d. 1300 mL

e. 100 mL

Watch Solution

What volume will 0.780 moles of Xe occupy at STP?

Watch Solution

A sample of helium (He) occupies 4 liters at STP. What pressure is necessary to change the volume to 2 liters at 20°C?

1. 2.1464 atm

2. 2.0 atm

3. 2.36 atm

4. 4.361 atm

5. 4.0 atm

Watch Solution

Standard conditions (STP) is defined as

1. 273.15 K, 760 torr.

2. 0 K, 250 atm.

3. 100 K, 1 torr.

4. 273.15 K, 250 torr.

5. 0 K, 1 atm.

Watch Solution

If 250 mL of a gas at STP weighs 2 g, what is the molar mass of the gas?

A. 179 g • mol^{-1}

B. 8.00 g • mol^{-1}

C. 56.0 g • mol^{-1}

D. 28.0 g • mol^{-1}

E. 44.8 g • mol^{-1}

Watch Solution

A balloon filled with helium occupies 20.0 L at 1.50 atm and 25°C. How many moles of helium will there be in the balloon at STP?

A. 22.4 moles

B. 1.12 moles

C. 0.0446 moles

D. 0.893 moles

E. 1.23 moles

F. 4.55 moles

Watch Solution

What volume will 40.0 L of He at 50.00°C and 1201 torr occupy at STP?

A. 26.7 L

B. 18.6 L

C. 12.8 L

D. 53.4 L

E. 31.1 L

Watch Solution

Calculate the density of nitrogen gas at STP.

A. 0.625 g/L

B. 1.25 g/L

C. 6.83 g/L

D. 13.7 g/L

E. Cannot be calculated with this information (undefined)

Watch Solution

What is the volume occupied at STP by a mixture of 4.00 g of He_{(g)}, 2.00 g of H_{2(g)} and 32.0 g of O_{2(g)}?

A. 6.15 L

B. 11.2 L

C. 22.4 L

D. 44.8 L

E. 67.2 L

Watch Solution

If the density of a gas 1.43 g/L at STP, what is the molecular weight of the gas?

Watch Solution

What volume will 3.12 grams of helium occupy at STP?

Watch Solution

Which of the following gases has the greatest density at STP?

A) NO_{2 }(molar mass = 46.01 g/mol)

B) Xe (molar mass = 131.3 g/mol)

C) SO_{2} (molar mass = 64.07 g/mol)

D) SF_{6} (molar mass = 146.07 g/mol)

E) All of these samples have the same density at STP.

Watch Solution

An ideal gas occupies 49.0 L at 994 torr and 41.0°C.

What volume would it occupy at STP?

1. 0.0136 L

2. 73.7 L

3. 55.7 L

4. 58.7 L

5. 105 L

6. 39.1 L

7. 69.9 L

8. 0.0179 L

9. 22.4 L

Watch Solution

The density of a gas is 1.96 g/L at STP. What would the mass of 2.00 moles of the gas be at STP?

1. 87.8 g

2. There is not enough information to solve.

3. 44.8 g

4. 0.0875 g

5. 43.9 g

6. 0.510 g

Watch Solution

Using the graph below, determine the gas that has the lowest density at STP.

A) A

B) B

C) C

D) D

E) All of the gases have the same density at STP.

Watch Solution

A hypothetical rock was harvested from another planet. Trapped inside was a diatomic gas. A volume of 1.25 mL of the gas was extracted from the rock at STP. The mass of the gas sample was determined to be 2.12 mg. Identify the gas.

1. oxygen

2. None of these

3. hydrogen

4. nitrogen

5. fluorine

Watch Solution

If sufficient acid is used to react completely with 21.0 grams of Mg

Mg(s) + 2HCl(aq) → MgCl_{2}(aq) + H_{2}(g)

what volume of hydrogen at STP would be produced?

1. 9.68 liters

2. 19.37 liters

3. 10.60 liters

4. 22.40 liters

5. 4.84 liters

Watch Solution

Lithium reacts with nitrogen gas according to the reaction:

6 Li(s) + N_{2}(g) → 2 Li_{3}N(s)

What mass of lithium (in g) reacts completely with 58.5 mL of N_{2} gas at STP?

Watch Solution

Automobile air bags inflate following a serious impact. The impact triggers the chemical reaction:

2 NaN_{3}(s) → 2Na(s) + 3 N_{2}(g)

If an automobile air bag has a volume of 11.8 L, what mass of NaN _{3} (in g) is required to fully inflate the air bag upon impact? Assume STP conditions.

Watch Solution

Use the molar volume of a gas at STP to calculate the density (in g/L) of nitrogen gas at STP.

Watch Solution

Use the molar volume of a gas at STP to determine the volume (in L) occupied by 33.6 g of neon at STP.

Watch Solution

A mixture of hydrogen and helium is 25.0% hydrogen by mass. What is the partial pressure of hydrogen (in atm) in the mixture at STP?

a) 0.460

b) 0.399

c) 0.520

d) 0.250

e) 0.380

Watch Solution

Assuming ideal behavior, what is the density of argon gas at STP, in g/L?

a) 0.0176 g/L

b) 0.0250 g/L

c) 1.63 g/L

d) 1.78 g/L

e) 181. g/L

Watch Solution

At STP what volume of N _{2} will react completely with 22.2 L H _{2} to produce NH_{3}?

N_{2}(g) + 3H_{2} (g) → 2NH _{3} (g)

a. 7.4 L

b. 14.8 L

c. 22.2 L

d. 44.4 L

e. 66.6 L

Watch Solution

Which gas sample has the greatest volume at STP?

a. 5g Ar

b. 5g Rn

c. 5g Ne

d. 5g Kr

e. 5g Xe

Watch Solution

A sample of N_{2} gas occupies a volume of 746 mL at STP. What volume would N _{2} gas occupy at 155°C at a pressure of 368 torr?

1. 983 mL

2. 566 mL

3. 3295 mL

4. 312 mL

5. 588 mL

6. 323 mL

7. 2415 mL

8. 1792 mL

Watch Solution

What is the density of Xe gas at STP? Give your result in g/L.

a. 0.00156

b. 64.0

c. 5.86

d. 5.37

e. 0.178

Watch Solution

How many moles of O _{2} (molar mass = 32.00 g/mol) are needed to react completely with 52.0 L of CH_{4}(g) at STP to produce CO _{2} and H_{2}O? (molar mass (CH _{4}) = 16.04 g/mol)

a) 11.6

b) 2.32

c) 4.64

d) 52.0

e) 104

Watch Solution

Which of the following gases has the highest density at STP?

A. sulfur trioxide, SO _{3}

B. carbon dioxide

C. NO _{2}

D. argon

E. nitrogen

Watch Solution