Boyle’s Law



Ideal Gas Law

PV = nRT

This formula is used when you have a gas and you are trying to find moles, volume, pressure, or temperature.

P = pressure n = number of moles

V = volume T = temperature in Kelvin

R = Universal Gas Constant

R = 0.0821 atm L R = 62.4 mmHg L

mol K mol K

1. Calculate the volume, in liters, of 2.15 moles oxygen gas at 298 K and 1.25 atm.

Step 1 List the information

P= 1.25atm n = 2.15moles

V= ? R = 0.0821 atm L

mol K

T = 298K

Step 2 Write down the formula

PV= nRT V= nRT

P

Step 3 Plug the numbers into the formula

(2.15moles)(298K)(0.0821atmL)

(1.25atm)(mole K)

Step 4 Report the answer

42.08 L

2. What are the values for the temperature and pressure at STP?

Pressure= 1 atm or 760 mmHg

Temperature= 0 oC or 273 Kelvin

3. What is the volume of 1 mole of a gas at 273 K and 1 atm?

V= nRT V= (1 mole)(0.0821 atm L)(273K) = 22.4L

P 1 atm (mole K)

4. If a 2.8 mole sample of gas initially occupies 54 L at 3.8 atm, what is its temperature in K?

T= PV T= (3.8 atm)(54 L) mole K = 892.6 K

nR (2.8 mole)(0.0821 atm L)

5. How many moles of gas are present if a particular sample occupies 2.94 L with a pressure and temperature of 450 torr and 315 K respectively?

n = PV n = (450 torr)(2.94 L) mole K = 0.0673 moles

RT (315 K)(62.4 torr L)

6. How many moles of gas are present in a 500 mL container at STP?

n = PV n = (1 atm)(0.5 L) mole K = 0.0223 moles

RT (273 K)(0.0821 atm L)

7. What is the temperature in oC if you have 4 moles of gas that occupy 224 L liters at 1 atm? (Remember to convert from K to oC)

T= PV T = (1 atm)(224 L) mole K = 682 K 409 oC

nR (4 mole)(0.0821 atm L)

8. How many moles of an ideal gas are in 1.0 mL if the temperature is -80 °C and the pressure is 0.0010 torr? (Remember to convert from oC to K)

n = (0.0010 torr)(0.001 L) mole K = 8.3 x 10-11 moles

(193 K)(62.4 torr L)

9. What is the volume of 1.2 moles of gas at 0.5 atm and 200 K?

V= nRT V = (1.2 mole)(0.0821 atm L)(200 K) = 39.4L

P 0.5 atm (mole K)

10. How many moles would be present under the following conditions 200 mL of gas at 800 torr are at 1000C?

n = (800 torr)(0.200 L) mole K = 0.00687 moles

(373 K)(62.4 torr L)

11. What is the pressure of gas if 5 moles occupies 2 liters at and 298 K?

P= nRT P = (5 mole)(0.0821 atm L)(298 K) = 61.16 atm

V 2 L (mole K)

12. What is the pressure of gas if 14.8 moles occupies 3.75 liters at and 32 °C? (Remember to convert from oC to K)

P= nRT P = (14.8 mole)(0.0821 atm L)(305 K) = 98.8 atm

V 3.75 L (mole K)

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