# Gas Stoichiometry Problems

TLDRThis tutorial comprehensively covers gas stoichiometry problems, focusing on the calculation of gas volumes and moles at standard temperature and pressure (STP). The video explains the concept of STP, where one mole of gas occupies 22.4 liters, and demonstrates conversions between moles and liters for gases. It then tackles a series of problems involving chemical reactions, including the decomposition of magnesium carbonate, the reaction between magnesium nitride and water, and the reaction of zinc with hydrochloric acid to produce hydrogen gas. Each problem is meticulously solved by first identifying the limiting reactant, then calculating the moles of products formed, and finally determining the volume or pressure of the gases produced under specified conditions. The tutorial also emphasizes the importance of using the ideal gas law (PV=nRT) for these calculations and provides step-by-step solutions to enhance understanding.

###### Takeaways

- π **Standard Temperature and Pressure (STP):** At STP, one mole of any ideal gas occupies a volume of 22.4 liters at a temperature of 0Β°C (273 K) and a pressure of 1 atm.
- π **Gas Stoichiometry:** The volume of a gas can be calculated using the Ideal Gas Law equation, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
- βοΈ **Molar Mass Calculation:** The molar mass of a compound is the sum of the atomic masses of all the atoms in its chemical formula.
- π **Mole-to-Liter Conversion:** At STP, moles and liters are proportional for gases, allowing for direct conversion using the factor that one mole of gas occupies 22.4 liters.
- π **Balanced Equations:** In chemical reactions, balanced equations ensure equal numbers of atoms for each element on both sides of the equation.
- π« **Limiting Reactant:** In a reaction, the limiting reactant is the substance that is completely consumed and determines the maximum amount of product that can be formed.
- π **Excess Reactant:** The reactant remaining after the limiting reactant is consumed; it does not affect the amount of product formed.
- π’ **Mole Calculation:** The number of moles can be calculated using the formula n = PV/RT, where P is pressure, V is volume, R is the gas constant, and T is temperature in Kelvin.
- π **Volume Calculation:** The volume of a gas produced in a reaction can be found by converting moles of the product to liters using the molar volume at STP (22.4 L/mol).
- π© **Chemical Formulas:** Understanding the charges of elements and polyatomic ions is crucial for writing correct chemical formulas and balanced equations.
- π **Ideal Gas Law Application:** The Ideal Gas Law is a fundamental principle used to calculate various properties of gases, including pressure, volume, and the number of moles.

###### Q & A

### What does SDP stand for in the context of gas stoichiometry problems?

-SDP stands for Standard Density and Pressure. It refers to the conditions of 0 degrees Celsius (273 Kelvin) and 1 atmosphere of pressure, where one mole of an ideal gas occupies a volume of 22.4 liters.

### How can you calculate the volume of 2.5 moles of argon gas at STP?

-Since one mole of gas occupies 22.4 liters at STP, the volume of 2.5 moles of argon gas can be calculated by multiplying 2.5 moles by 22.4 liters/mole, which equals 56 liters.

### What is the balanced chemical reaction for the combustion of propane?

-The balanced chemical reaction for the combustion of propane (C3H8) with oxygen gas (O2) is 3 C3H8 + 5 O2 β 3 CO2 + 4 H2O, producing carbon dioxide and water.

### If 8.4 liters of O2 reacts with excess propane, how many liters of CO2 are produced?

-Using the molar ratio of O2 to CO2, which is 5:3, 8.4 liters of O2 will produce 8.4 * (3/5) = 5.04 liters of CO2.

### What is the volume of CO2 gas produced at STP from the decomposition of 7.45 grams of magnesium carbonate?

-First, calculate the moles of MgCO3 (7.45 g / 84.315 g/mol), then since the molar ratio of MgCO3 to CO2 is 1:1, the moles of CO2 produced will be the same. Finally, convert moles of CO2 to volume at STP (moles * 22.4 L/mol) to get approximately 1.98 liters of CO2.

### How many grams of magnesium nitride are consumed when 4.7 liters of ammonia gas is collected at 300 Kelvin and 1.6 atm?

-Calculate the moles of NH3 using the ideal gas law (PV = nRT), which gives 0.3055 moles of NH3. Since the molar ratio of NH3 to Mg3N2 is 2:1, 0.3055 moles of NH3 corresponds to 0.3055/2 moles of Mg3N2. With a molar mass of Mg3N2 of 100.935 g/mol, the mass of Mg3N2 consumed is (0.3055/2) * 100.935 g β 15.42 grams.

### How do you determine the limiting reactant in a reaction?

-To determine the limiting reactant, calculate the moles of each reactant and then compare the mole per coefficient ratio from the balanced chemical equation. The reactant with the lowest ratio is the limiting reactant.

### What is the volume of N2 produced when 4.85 liters of NH3 at 27Β°C and 1.5 atm is mixed with 5.23 liters of O2 at 32Β°C and 1.63 atm?

-First, find the moles of NH3 and O2 using the ideal gas law. NH3 is the limiting reactant with a mole ratio of 4:2 to N2. Calculate the moles of N2 produced (0.2857 moles NH3 * 2/4) and then use the ideal gas law to find the volume of N2 at the new conditions (37Β°C and 1.52 atm), which is approximately 2.392 liters.

### How do you calculate the pressure of H2 gas produced when 24 grams of zinc reacts with 245 mL of a 1.75 M HCl solution?

-Calculate the moles of Zn and HCl, identify the limiting reactant (HCl in this case), and use the stoichiometry of the reaction (1 mole Zn reacts with 2 moles HCl to produce 1 mole H2) to find moles of H2. Then use the ideal gas law PV = nRT to calculate the pressure of H2 at the given volume (0.5 L) and temperature (298 K), which is 10.49 atm.

### What is the molar mass of magnesium carbonate (MgCO3) in grams per mole?

-The molar mass of MgCO3 is calculated by adding the atomic masses of its constituent elements: magnesium (24.305 g/mol), carbon (12.01 g/mol), and oxygen (3 atoms * 16.00 g/mol). The total molar mass is 24.305 + 12.01 + (3 * 16.00) = 84.315 g/mol.

### How can you convert the mass of a substance to moles using its molar mass?

-To convert the mass of a substance to moles, divide the mass of the substance (in grams) by its molar mass (in grams per mole). The result is the number of moles of the substance.

###### Outlines

##### π§ͺ Gas Stoichiometry and the Ideal Gas Law

This paragraph introduces the concept of gas stoichiometry and the use of the Ideal Gas Law (pv = nrt) to calculate volumes at Standard Temperature and Pressure (STP). It explains that at STP, one mole of gas occupies 22.4 liters. The paragraph also covers the calculation of the volume occupied by 2.5 moles of argon gas at STP, which is 56 liters, and the conversion between moles and liters for gases. Additionally, it presents a problem involving the reaction of propane with oxygen to produce carbon dioxide and water, and how to calculate the volume of CO2 produced from a given volume of O2.

##### π Balanced Equations and Conversions in Chemistry

The second paragraph focuses on writing balanced chemical equations and performing conversions between grams and moles, and between moles and liters for gases. It discusses the decomposition of magnesium carbonate to carbon dioxide and magnesium oxide, and how to calculate the volume of CO2 produced at STP from a given mass of magnesium carbonate. The paragraph also covers the reaction of magnesium nitride with water to produce ammonia gas and magnesium hydroxide, and how to determine the amount of magnesium nitride consumed to produce a certain volume of ammonia gas at specific conditions.

##### π§ͺ Calculations Involving the Ideal Gas Law

This paragraph delves into the use of the Ideal Gas Law (pv = nrt) for calculating the moles of a gas and subsequently its volume. It covers the reaction of magnesium nitride with water to form ammonia and magnesium hydroxide, emphasizing the identification of the limiting reactant. The paragraph explains how to calculate the moles of NH3 produced and then use that to find out how many grams of magnesium nitride were consumed. It also discusses the reaction of ammonia gas with oxygen gas to produce water and nitrogen gas, and how to determine the volume of N2 produced under specified conditions.

##### π¬ Chemical Reactions and Limiting Reactants

The fourth paragraph discusses the importance of identifying the limiting reactant in a chemical reaction. It presents a scenario where ammonia reacts with oxygen to produce water and nitrogen gas, and explains how to calculate the volume of nitrogen gas produced. The paragraph emphasizes the need to balance the chemical equation and use the stoichiometric ratios to perform the calculations. It also covers the conversion of moles of reactants to moles of products using the Ideal Gas Law, and how to adjust for different temperatures and pressures.

##### π§ͺ Reaction of Zinc with Hydrochloric Acid

This paragraph covers the reaction between zinc and hydrochloric acid to produce hydrogen gas and aqueous zinc chloride. It explains the process of balancing the chemical equation and identifying the limiting reactant by comparing the mole per coefficient ratio of the reactants. The paragraph details the calculation of moles of each reactant from their mass and concentration, and how to determine the moles of hydrogen gas produced based on the limiting reactant. It concludes with the calculation of the pressure of hydrogen gas collected under specific conditions using the Ideal Gas Law.

##### π Conversion of Units and Calculation of Pressure

The final paragraph focuses on the conversion of units from milliliters to liters and from Celsius to Kelvin as required for the Ideal Gas Law calculations. It discusses the calculation of the pressure of hydrogen gas produced from the reaction of zinc with hydrochloric acid. The paragraph emphasizes the need to use the correct values for the gas constant (r) and to ensure that all measurements are in consistent units. It concludes with the calculation of the pressure of hydrogen gas, resulting in a final answer of 10.49 atm.

###### Mindmap

###### Keywords

##### π‘Gas Stoichiometry

##### π‘Standard Temperature and Pressure (STP)

##### π‘Ideal Gas Law

##### π‘Molar Volume

##### π‘Combustion Reaction

##### π‘Decomposition Reaction

##### π‘Limiting Reactant

##### π‘Mole-to-Mole Conversion

##### π‘Chemical Formula

##### π‘Molar Mass

##### π‘Temperature Conversion

###### Highlights

Gas stoichiometry problems are discussed in the tutorial

Standard temperature and pressure (STP) defined as 0Β°C and 1 atm

At STP, one mole of gas occupies a volume of 22.4 liters

Ideal gas law equation PV = nRT used to prove the volume of one mole of gas

Conversion factor: 1 mole of gas = 22.4 liters at STP

Volume of 2.5 moles of argon gas at STP calculated to be 56 liters

Conversion factor used to convert moles to liters and vice versa for gases

175 liters of oxygen gas at STP corresponds to 7.81 moles of O2

Balanced chemical equation for propane reacting with oxygen to form CO2 and H2O

8.4 liters of O2 reacts with excess propane to produce 5.04 liters of CO2

MgCO3 decomposes into CO2 and MgO when heated, producing 1.98 liters of CO2 gas at STP

Mg3N2 reacts with H2O to produce NH3 and Mg(OH)2, with balanced chemical equation

4.7 liters of NH3 gas collected at 300 K, 1.6 atm corresponds to 15.42 grams of Mg3N2 consumed

Balanced chemical equation for NH3 reacting with O2 to form N2 and H2O

2.39 liters of N2 gas produced when 4.85 liters of NH3 at 27Β°C, 1.5 atm reacts with 5.23 liters of O2 at 32Β°C, 1.63 atm

24 grams of Zn reacts with 245 mL of 1.75 M HCl solution to produce H2 gas and ZnCl2

HCl is the limiting reactant, with 0.2144 moles of H2 gas produced

Pressure of H2 gas collected in a 500 mL test tube at 25Β°C calculated to be 10.49 atm

###### Transcripts

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