Activity 151-13 Ideal Gas Law Directions: This GLA worksheet discusses the Ideal Gas Law equation. Part A introduces the variables in an Ideal Gas Law word problem and converting units. Part B discusses utilizing the Ideal Gas Law equation to solve a word problem. Part C discusses standard temperature and pressure (STP) conditions of a gas. The worksheet is accompanied by instructional videos. See http://www.canyons.edu/Departments/CHEM/GLA/ for additional materials. Part A – The Basics A gas is different than a liquid or solid because the atoms or molecules in a gas are very far apart from each other and are moving very fast. The properties of gases are affected by pressure, temperature, volume, and amount of gas atoms or molecules present. The Ideal Gas Law equation relates these variables with a constant, R: Ideal Gas Law:
PV = nRT
P = pressure in atmosphere (atm) V = volume in Liters n = number of moles of the gas T = temperature in units Kelvin (K) R = ideal gas constant, 0.08206
𝐿∙𝑎𝑡𝑚 𝑚𝑜𝑙∙𝐾
When using the Ideal Gas Law, the units of each of the variables needs to be the same as that of the ‘R’ constant because they need to be able to cancel. In order to utilize the Ideal Gas Law equation, we need to be able to identify the variables in a word problem and convert units if necessary. For additional guidance, consult the “Unit Conversion” and “Dimensional Analysis” GLA worksheets. In each of the following word problems, identify each of the variables and convert units, if necessary, to match the units of the ‘R’ constant. For any variable not given, write ‘??’ to indicate it is unknown. Examples: a) A container holds 118 mL of air at a total pressure of 55.7 psi and a temperature of 30.0 C. How many moles of gas are in the container? Step 1. Identify each of the variables P = 55.7 psi V = 118 mL
n = ?? T = 30.0 C
R = ideal gas constant, 0.08206
Chemistry Guided Learning Activities Activity 151 – 13
𝑳∙𝒂𝒕𝒎 𝒎𝒐𝒍∙𝑲
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Step 2. Convert any units, if necessary, to match the units of the ‘R’ constant. Pressure (P): 𝟏 𝒂𝒕𝒎 𝟓𝟓. 𝟕 𝒑𝒔𝒊 ( ) = 𝟑. 𝟕𝟖𝟗𝟏𝟏𝟓𝟔 𝒂𝒕𝒎 𝟏𝟒. 𝟕 𝒑𝒔𝒊
Volume (V): 𝟏𝑳 𝟏𝟏𝟖 𝒎𝑳 ( ) = 𝟎. 𝟏𝟏𝟖 𝑳 𝟏𝟎𝟎𝟎 𝒎𝑳
Temperature (T): 𝟑𝟎. 𝟎 𝑪 + 𝟐𝟕𝟑. 𝟏𝟓 = 𝟑𝟎𝟑. 𝟏𝟓 𝑲
Practice: a) What is the pressure (in mm Hg) of 0.0320 mol of neon gas with a volume of 535 mL at 30 C? Step 1. Identify each of the variables 0.0320 mol ?? P = ___________ n = ___________ 535 mL V = ___________
R = ideal gas constant, 0.08206
30 oC T = ___________ 𝐿∙𝑎𝑡𝑚 𝑚𝑜𝑙∙𝐾
Step 2. Convert any units, if necessary, to match the units of the ‘R’ constant.
Part B – Utilizing the Ideal Gas Law Once the variables have been identified and converted into the correct units, they can be utilized in the Ideal Gas Law equation. Note that the Ideal Gas Law equation relates moles of a gas. If we would like to find grams of a gas, we need to use the molar mass of the gas to convert from moles to grams. Refer to the “Mole Conversions” GLA 151-8 worksheet for additional guidance. Examples: a) What is the volume occupied by 0.900 g of helium gas at 987 mm Hg and 32 C? Step 1. Identify each of the variables P = 987 mm Hg V = ??
n = 0.900 g T = 32 C
R = ideal gas constant, 0.08206 Chemistry Guided Learning Activities Activity 151 – 13
𝑳∙𝒂𝒕𝒎 𝒎𝒐𝒍∙𝑲
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Step 2. Convert any units, if necessary, to match the units of the ‘R’ constant. Pressure (P): 𝟏 𝒂𝒕𝒎 𝟗𝟖𝟕 𝒎𝒎 𝑯𝒈 ( ) = 𝟏. 𝟐𝟗𝟖𝟔𝟖 𝒂𝒕𝒎 𝟕𝟔𝟎 𝒎𝒎 𝑯𝒈
Moles (n): 𝟏 𝒎𝒐𝒍 𝟎. 𝟗𝟎𝟎 𝒈 ( ) = 𝟎. 𝟐𝟐𝟓 𝒎𝒐𝒍 𝟒. 𝟎𝟎 𝒈
Note that we used the molar mass of He to convert from grams to moles.
Temperature (T): 𝟑𝟐. 𝟎 𝑪 + 𝟐𝟕𝟑. 𝟏𝟓 = 𝟑𝟎𝟓. 𝟏𝟓 𝑲
Step 3. Since we are solving for volume (V), we can rearrange the equation by dividing both sides of the equation by P: 𝑷𝑽 𝒏𝑹𝑻 = 𝑷 𝑷
Plug in the known values and solve: 𝑳 ∙ 𝒂𝒕𝒎 (𝟎. 𝟐𝟐𝟓 𝒎𝒐𝒍) (𝟎. 𝟎𝟖𝟐𝟎𝟔 ) (𝟑𝟎𝟓 𝑲) 𝒏𝑹𝑻 𝒎𝒐𝒍 ∙𝑲 𝑽 = = = 𝟒. 𝟑𝟑 𝑳 𝑷 𝟏. 𝟐𝟗𝟖𝟔𝟖 𝒂𝒕𝒎
Notice that the units in the calculation cancelled to leave the units of Liters, which is a volume unit. This can be used to check that the problem has been solved correctly.
Practice: a) Carbon dioxide (CO2) in a 250. mL container is held at a pressure of 855 torr and 30 C. How many grams of CO2 are present in the container? Step 1. Identify each of the variables. P = ___________
n = ___________
V = ___________
T = ___________
R = ideal gas constant, 0.08206
𝐿∙𝑎𝑡𝑚 𝑚𝑜𝑙∙𝐾
Step 2. Convert any units, if necessary, to match the units of the ‘R’ constant.
Chemistry Guided Learning Activities Activity 151 – 13
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Step 3. Since we are solving for __________, we can rearrange the equation by dividing both sides of the equation by __________: 𝑃𝑉 = 𝑛𝑅𝑇
Plug in the variables and cancel units:
L-atm/mol K
K
Step 4. Use the molar mass of CO2 to convert from moles to grams.
Part C – Standard Temperature and Pressure (STP) Standard temperature and pressure (STP) conditions are conditions in which we define standard temperature (T) to be 0 C (273.15 K) and standard pressure to be 1 atm. Under STP conditions, 1 mol of any ideal gas will have a volume of 22.4 L. This volume can be derived using the Ideal Gas Law Equation: 𝑳 ∙ 𝒂𝒕𝒎 (𝟏 𝒎𝒐𝒍) (𝟎. 𝟎𝟖𝟐𝟎𝟔 ) (𝟐𝟕𝟑. 𝟏𝟓 𝑲) 𝒏𝑹𝑻 𝒎𝒐𝒍 ∙𝑲 𝑽 = = = 𝟐𝟐. 𝟒 𝑳 𝑷 𝟏 𝒂𝒕𝒎 This relationship can then be used to convert amount of gas to volume of gas under STP conditions. We can use it as a conversion factor instead of using the Ideal Gas Law equation. 𝟏 𝒎𝒐𝒍 = 𝟐𝟐. 𝟒 𝑳 Example: a) Determine the volume of 0.545 mol of CO2 gas at STP. 𝟐𝟐. 𝟒 𝑳 𝟎. 𝟓𝟒𝟓 𝒎𝒐𝒍 ( ) = 𝟏𝟐. 𝟐 𝑳 𝟏 𝒎𝒐𝒍
b) How many grams of SO2 gas are contained in a 372 mL container at STP? 𝟏 𝑳 𝟏 𝒎𝒐𝒍 𝟔𝟒. 𝟎𝟔𝟔 𝒈 𝟑𝟕𝟐 𝒎𝑳 ( )( )( ) = 𝟏. 𝟎𝟔 𝒈 𝟏𝟎𝟎𝟎 𝒎𝑳 𝟐𝟐. 𝟒 𝑳 𝟏 𝒎𝒐𝒍
Chemistry Guided Learning Activities Activity 151 – 13
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Practice: a) Determine the volume (in mL) of 2.70 mol of CH4 gas at STP.
b) How many grams of N2 gas are contained in a 500. mL container at STP?
Chemistry Guided Learning Activities Activity 151 – 13
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Part D – Extra Practice a) What is the volume occupied by 0.225 mol of helium gas at 987 mm Hg and 305 K? b) A container holds 525 mL of H2 gas at a total pressure of 45.0 psi and a temperature of 20 C. How many grams of H2 are in the container? c) How many grams of Cl2 gas are contained in a 625 mL cylinder at 25 C and 756 mm Hg? d) What is the volume of 2.35 g of carbon monoxide (CO) gas at 45 C and 850 torr? e) What is the pressure (in torr) of 0.563 mol of a gas contained in a 2.00 L container at 55 C? f) Neon (Ne) gas is held in a 375 mL container at STP. How many grams of Ne are present? g) A 50.0 mL balloon is filled with Helium (He) gas at STP. How many grams of He are contained within the balloon? Challenge problem a) A sample of gas has a mass of 0.450 g. Its volume is 112 mL at a temperature of 65 C and a pressure of 765 mm Hg. Find the molar mass of the gas.
Chemistry Guided Learning Activities Activity 151 – 13
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