Ideal gas law problems with answers?

Answer 1

PV equals nRTThe Ideal Gas Law is used to relate the pressure, volume, temperature and amount of an "ideal" gas. Although many gases are not perfectly ideal in reality, you can usually use the Ideal Gas Law anyway. Here is how you solve these problems!

The Ideal Gas Law is: PV = nRT.

Where:

-- P is the pressure of the gas (in atmospheres, ATM)

-- V is the volume of the container (in liters, L)

-- n is the number of moles of gas in the container (in moles, mol)

-- R is Universal Gas Constant (which is 0.0820574587 L · ATM · K-1 · mol-1)

-- T is the temperature of the gas (in Kelvin)

In English that says that pressure times the volume equals the number of moles times the Gas Constant times the temperature. It also means that pressure and volume are inversely proportional. Also it means the temperature is directly proportional to both the pressure and the volume. The amount of substance is directly proportional to the volume and the pressure.

-SO HOW DO YOU USE IT?

First, you need to figure out what you know from the question, and what you need to find. Since "R" is just a known constant, the Ideal Gas Law has only 4 variables in it: P, V, n, and T. In order to use this equation to solve for something, you must know at least 3 of these! Figure out which ones you know. Be careful, sometimes the units will not be the same as what I've written above. For instance, if you have the number of grams of a substance, that can be used to find the number of moles (if you know the molar mass), which give you the variable "n." Once you know what you are solving for, isolate that variable by rearranging the equation. Here are some examples:

To solve for the number of moles, we have: n =PV/RT

or to solve for the temperature, we have: T =PV/nR

or to solve for the pressure, we have: P =nRT/V

or finally, to solve for the volume, we have: V =nRT/P

Now, we MUST make sure everything is in the correct units before we solve!

PRESSURE (P): The unit of pressure must be in units of ATM. The units of pressure can be given in many different units. However, to use the Ideal Gas Law, the best unit to use is called an atmosphere, written "ATM." Here is how to convert from other units of pressure to ATM:

1 ATM = 14.6959488 pounds per square inch (psi)

1 ATM = 29.9246899 inches of Mercury (in Hg)

1 ATM = 760 mm mercury (mm Hg)

1 ATM = 760 torr (torr)

1 ATM = 101,325 pascals (Pa)

1 ATM = 101.325 kilopascals (kPa)

1 ATM = 1.01325 bar (bar)

If you see any of these other units of pressure being used, convert them to ATM using the factor given above.

--For example, if the problem give the pressure as 30.2 in Hg, do this:

30.2 in Hg ÷ 29.9247 in Hg/ATM = 1.009 ATM

-VOLUME (V): The volume must be in units of liters (L). Here are is the conversion from some other standard units of volume:

1 L = 1000 milliliters (mL)

1 L = 1000 cubic centimeters (cm3)

1 L = 1 cubic decimeter (dm3)

1 L = 0.001 cubic meters (m3)

1 L = 0.264172051 US gallons (G)

1 L = 1.0566882 US quarts (Q)

--For example, if the volume is 1 gallon, do this:

1 gallon ÷ 0.26417 G/L = 3.785 L

-NUMBER OF MOLES (n): The number of moles must be in units of moles. If not given in terms of moles, the most common way is to give it in number of grams. To go from grams to moles, divide the number of grams by the molar mass (MM) of the substance. Use the Periodic Table to calculate the molar mass.

number of grams / molar mass = number of moles

--For example, if there are 10 g of water, do this:

The molecular formula for water is H2O. The molar mass is then two times the molar mass of H plus the molar mass of O:

2*1.008 + 15.999 = 18.015 grams per mole

If there are 10 grams, to convert that to moles:

10 g ÷ 18.015 g/mol = .5551 moles

-UNIVERSAL GAS CONSTANT (R): You want to use this value: 0.0820574587 L · ATM · K-1 · mol-1. There are several different values of the Universal Gas Constant, but the only difference is what units they are in. Make sure you use the correct value. If you use another value, the other units will not match up correctly.

-TEMPERATURE (T): The units of temperature must be in Kelvin. You cannot use Centigrade (Celsius) or Fahrenheit. To convert:

-From degrees Celsius: add 273.15 to get Kelvin

-From degrees Fahrenheit: convert to Celsius first, then follow instructions above. To convert °F to °C, use this method:

-first subtract 32 from the °F number

-then divide that number by 9

-then multiply that by 5

Don't forget to convert °C to Kelvin afterwards!

--For example, if the temperature is 75 °C, in Kelvin that is:

75 °C + 273.15 = 348.15 K

Or instead, if the temperature is given as 150 °F, do this:

150 - 32 = 118

118 ÷ 9 = 13.111

13.111 * 5 = 65.556 °C

Then to get Kelvin: 65.556 °C + 273.15 = 338.706

-Once you've made sure all the units are correct, just plug in to the equation where you isolated the variable you want to find, and solve!

-- FINAL NOTE: Some questions say that the conditions are "at STP." That means that they are at Standard Temperature and Pressure.

-Standard temperature is equal to 0 °C, which is 273.15 K.

-Standard pressure is equal to 1 ATM.

ALSO: See the Related Questions links to the left of this answer. There are some example problems that have been solved correctly and show the details of the work. After reading this, look at those examples.

Answer 2

Find the final pressure of gas at 150 K, if the pressure of gas is 210 kPa at 120 K.

GIVEN:

P1= 210 kPa T1= 120 K

P2= ? T2= 150 K

SOLUTION:

Formula:

P2= P1xT2/T1

= (210 kPa) (150 K) / 120 K

P2= 262.5 kPa

Answer 3

Sure, here is an example ideal gas law problem and its solution:

Problem: If 2.5 moles of a gas are at a pressure of 3 atm and a volume of 10 L, what is the temperature of the gas in Kelvin? (R = 0.0821 L·atm/mol·K)

Solution: The ideal gas law is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature. Rearranging the equation to solve for T gives T = (PV) / (nR). Plugging in the values, we get T = (3 atm * 10 L) / (2.5 mol * 0.0821 L·atm/mol·K) = 144.58 K.

Answer 4

Solving a combined gas law problem is extremely easy. All you do is plug in what you are given into a formula and the substitute x for what you are trying to find. The formula for the combined gas law is :

(P1*V1)/T1 = (P2*V2)/T2, where:

P1 = initial pressure

V1 = initial volume

T1 = initial temperature (in kelvins)

P2 = final pressure

V2 = final volume

T2 = final temperature

Here's a problem:

Suppose you have a gas with a volume of 45 L at a temperature of 89 degrees Celsius and pressure of 4 atm. When I decrease the temperature to 72 degrees Celsius and the pressure to 3 atm, what is the final volume of the gas?

OK, well, let's see what we are given here: we know the initial volume, pressure and temperature. Remember that for any gas law problem, you must ALWAYS convert to kelvins, otherwise your answer will be wrong. To convert from Celsius to Kelvin, add 273 to the Celsius value. So, 85 Celsius is 358 Kelvin. Now let's begin plugging what we know into the formula. You should get this:

(4*45)/358 = (P2*V2)/T2

We also know some of the final values (pressure and temperature), so plug those in too to get this, but remember to substitute x for the final volume, because that is what we are trying to find and also convert 72 Celsius to Kelvin. This is what you should have set up for your equation:

(4*45)/358 = (3*x)/345

Now simplify the equation to get this: 180/358 = 3x/345

Now, in order to solve for x, we need to cross multiply. To cross multiply, you take the numerator of the first fraction and times it by the denominator of the second fraction and take the numerator of the second fraction and times it by the denominator of the first fraction. After you cross multiple, you should get this simplified equation:

62,100 = 1,074x

Now, all that's left to do is divide by 1,074 on both sides of the equation to get x. So:

x = 57.82

Remember that when you get a value you must have it in the correct units. At the beginning of the problem, we are said that we have 45 L of a gas, so our final answer would be 57.82 L.

Hope this helped :)

Answer 5

You can derive the ideal gas law from assumptions about masses of particles, velocity of particles, collisions, pressure, and temperature, but you can't "prove" it since it only an approximation of the real world that breaks down when you get to temperatures that are too low, pressures that are too high, or encounter phase changes.

Answer 6

Solving ideal gas law problems is extremely easy. To begin, let's see what the formula for the ideal gas law is and what its terms mean.

PV = nRT, where:

P = pressure

V = volume

n = number of moles of a gas

R = 0.0821 L*atm/mol*K OR 8.315 dm^3 kPA/mol*K

T = temperature

Here's a problem:

If I have 4 moles of a gas at a pressure of 5.6 atm and a volume of 12 liters, what is the temperature?

To begin, I should elaborate on what to plug in for R. As a rule of thumb, if you are given liters of a gas, use the first value of R. If you are given a value in dm^3 (decameters cubed), use the second value.

So, first we need to know what we are given and what we don't know (what we are trying to find). We know P = 5.6, V = 12, n = 4, we know that we are using R = 0.0821 because we are given a volume in liters, and we also know that T = x (because we are trying to find the temperature).

So, let's set up our equation, plugging everything we know into it. You should get this:

(5.6)(12) = (4)(0.0821)(x)

Now, let's simplify the equation to get this:

67.2 = 0.3284x

To solve for x, divide by 0.3284 on each side of the equation. After doing this, you should get:

x = 204.63

So the temperature of the gas is 204.63 Kelvin. Remember that for any gas law problem, temperature is ALWAYS in Kelvin. If they wanted you to give the temperature in Celsius, you would subtract the temperature in Celsius from 273. So, if I were to ask for the temperature of this problem in Celsius, you would give me 68.37 Celsius.

Hope this helped clear things up :)

Answer 7

Gases, volume, pressure, moles and temperature are all related by the following equation:

pV=nRT

• P is pressure of the gas in Pascals (Pa)
• V is volume in m^3
• n is number of Moles of the gas
• R is the Gas Constant, 8,31 Jk^-1mol^-1
• T is temperature in Kelvin (K)

Tip: Always watch the units - you will often have to convert them.

At room temperature and pressure, 1 mole of any gas occupies the same volume.

This volume is 24,000cm^3 or 24dm^3

Volume(cm^3) = moles x 24,000 or Volume(dm^3) = moles x 24

You will often be asked how many litres there are in a certain gas:

1dm^3 = 1 Litre

Answer 8

That's not a question, and if I attempt to make it one, then it's unanswerable. Perhaps you should read your textbook. The ideal gas law is one of the simplest concepts in chemistry; if you can't understand it, you should look into getting a tutor.

Answer 9

Ideal gas law can be determined by figuring out the temperature, pressure, and volume of the gas. An equation to demonstrate this law is PV = nRT.

Answer 10

http://misterguch.brinkster.net/gaslawworksheets.html

Practice is the key to mastering this. Good for you.