Chapter 1: Problem 31
\(4.4\) g of an unknown gas occupies \(2.24\) litres of volume at STP. The gas may be (1) carbon dioxide (2) carbon monoxide (3) oxygen (4) sulphur dioxide
Short Answer
Expert verified
The unknown gas is carbon dioxide.
Step by step solution
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Molar Volume
When dealing with gases, especially in exercises involving the ideal gas law, you'll often use the concept of molar volume. Molar volume is the volume that one mole of any ideal gas occupies at Standard Temperature and Pressure (STP).
At STP, which is defined as 0°C (273.15 K) and 1 atm pressure, one mole of an ideal gas occupies 22.4 liters. This is extremely useful because it allows you to easily convert between the volume of gas and the amount in moles.
Understanding molar volume can make problems like the one described in the exercise much simpler. Once you know the volume of a gas at STP, you can quickly find out how many moles that volume represents using the 22.4 liters per mole relationship.
This becomes the foundation for further calculations, such as determining the molar mass of the gas.
At STP, which is defined as 0°C (273.15 K) and 1 atm pressure, one mole of an ideal gas occupies 22.4 liters. This is extremely useful because it allows you to easily convert between the volume of gas and the amount in moles.
Understanding molar volume can make problems like the one described in the exercise much simpler. Once you know the volume of a gas at STP, you can quickly find out how many moles that volume represents using the 22.4 liters per mole relationship.
This becomes the foundation for further calculations, such as determining the molar mass of the gas.
Molar Mass Determination
The molar mass of a substance is the mass of one mole of that substance. In many exercises, including the one given, you may need to determine the molar mass to identify an unknown gas.
Knowing both the mass of the gas and the volume it occupies (at STP) enables this calculation:
This molar mass can then be compared with known values to identify the gas, confirming it's carbon dioxide (CO₂) with a molar mass of 44 g/mol.
Knowing both the mass of the gas and the volume it occupies (at STP) enables this calculation:
- First, use the molar volume to find the number of moles of the gas.
- Then, use the mass of the gas and the number of moles to find the molar mass.
This molar mass can then be compared with known values to identify the gas, confirming it's carbon dioxide (CO₂) with a molar mass of 44 g/mol.
Mole Concept
The mole is a fundamental concept in chemistry that allows chemists to count entities (like atoms, molecules, and ions) by weighing them. One mole is defined as exactly 6.022 x 10²³ entities (Avogadro’s number).
This concept is particularly useful because it connects the macroscopic world that we can measure (like grams and liters) to the microscopic world of atoms and molecules.
In gas calculations, knowing the number of moles can be crucial for determining properties like volume, pressure, and temperature. In our problem, the volume of the gas and its relation to molar volume directly gave us the number of moles. This connection helps solve various other parameters and identify unknown gases by their molar masses.
This concept is particularly useful because it connects the macroscopic world that we can measure (like grams and liters) to the microscopic world of atoms and molecules.
In gas calculations, knowing the number of moles can be crucial for determining properties like volume, pressure, and temperature. In our problem, the volume of the gas and its relation to molar volume directly gave us the number of moles. This connection helps solve various other parameters and identify unknown gases by their molar masses.
Chemical Identification
Identifying a chemical substance involves knowing its properties and comparing them with known standards. For gases, one of the most telling properties is the molar mass.
In exercises like the given one, once you have determined the molar mass of the gas, you can compare it with the molar masses of possible candidates. In this case, a molar mass of 44 g/mol narrows it down to carbon dioxide (CO₂) among the given options.
This method of identification is efficient because it relies on a fundamental property (molar mass) that is consistent and unique for each substance. By using the data given (mass and volume at STP) alongside the mole concept, you get a reliable way to pin down what the gas actually is.
In summary, chemical identification combines these core concepts, enabling students to solve for and verify the identity of unknown substances.
In exercises like the given one, once you have determined the molar mass of the gas, you can compare it with the molar masses of possible candidates. In this case, a molar mass of 44 g/mol narrows it down to carbon dioxide (CO₂) among the given options.
This method of identification is efficient because it relies on a fundamental property (molar mass) that is consistent and unique for each substance. By using the data given (mass and volume at STP) alongside the mole concept, you get a reliable way to pin down what the gas actually is.
In summary, chemical identification combines these core concepts, enabling students to solve for and verify the identity of unknown substances.
