Problem 43
Question
At STP, \(0.280 \mathrm{~L}\) of a gas weighs \(0.400 \mathrm{~g}\). Calculate the molar mass of the gas.
Step-by-Step Solution
Verified Answer
The molar mass of the gas is \(32 \mathrm{~g/mol}\).
1Step 1: Understanding the problem
We have the volume (0.280 L) and the weight (0.400 g) of the gas at STP. We know that molar volume of any ideal gas at STP is \(22.4 \mathrm{~L/mol}\). The molar mass is defined as the mass of one mole of a substance and it is measured in g/mol. So, we need to find out how many moles are there in 0.280 L and then calculate the mass of that amount of gas in grams. This will yield us the molar mass.
2Step 2: Calculate the moles of the gas
We have the volume of the gas (0.280 L) and we know that molar volume of any ideal gas at STP is \(22.4 \mathrm{~L/mol}\). Therefore, the number of moles(n) of this gas can be calculated as follows: \(n = \frac{Volume~of ~gas}{Molar~volume~at~STP} = \frac{0.280~L}{22.4~L/mol} = 0.0125~mol\)
3Step 3: Calculate the molar mass
Molar mass is the mass of 1 mole of a substance. We know the mass of 0.0125 moles of this gas (which is 0.400 g). Therefore, the molar mass(M) of this gas can be calculated as follows: \(M = \frac{Mass~of ~gas}{number~of~moles} = \frac{0.400~g}{0.0125~mol} = 32~g/mol\). Thus, the molar mass of the gas is \(32 \mathrm{~g/mol}\).
Key Concepts
STP ConditionsIdeal Gas LawMolar VolumeGas Calculations
STP Conditions
STP stands for Standard Temperature and Pressure. It is a standard set of conditions for measuring the properties of gases. At STP, the temperature is exactly 0 degrees Celsius (273.15 Kelvin), and the pressure is 1 atmosphere (101.3 kPa). These conditions make calculations with gases easier and more consistent.
In the realm of chemistry, using STP allows scientists and students alike to predict how gases will behave under these unvarying conditions. This becomes very helpful when performing calculations related to volume, pressure, and temperature of gases, as it provides a simplified reference point.
When you're told a gas is at STP, you can assume it will follow predictable patterns described by gas laws, making gas calculations more straightforward.
In the realm of chemistry, using STP allows scientists and students alike to predict how gases will behave under these unvarying conditions. This becomes very helpful when performing calculations related to volume, pressure, and temperature of gases, as it provides a simplified reference point.
When you're told a gas is at STP, you can assume it will follow predictable patterns described by gas laws, making gas calculations more straightforward.
Ideal Gas Law
The Ideal Gas Law is a key principle in understanding how gases behave. It combines several simpler gas laws into one comprehensive equation:
\[ PV = nRT \]
Where:
While it provides a good approximation for many gases under a wide range of conditions, its predictions are most accurate at STP. The Ideal Gas Law is a cornerstone of gas calculations, helping us transition from theory to practice.
\[ PV = nRT \]
Where:
- \(P\) is the pressure
- \(V\) is the volume
- \(n\) is the number of moles
- \(R\) is the ideal gas constant
- \(T\) is the temperature in Kelvin
While it provides a good approximation for many gases under a wide range of conditions, its predictions are most accurate at STP. The Ideal Gas Law is a cornerstone of gas calculations, helping us transition from theory to practice.
Molar Volume
The molar volume of a gas is the volume that one mole of a substance occupies under specific conditions. At STP, the molar volume is approximately 22.4 liters for an ideal gas.
This concept is crucial because it allows us to relate the amount of gas (in moles) to the volume it occupies when it's at STP. Knowing the molar volume simplifies gas calculations, especially when determining the number of moles in a given volume.
For example, if we have 0.280 L of a gas at STP, dividing by the molar volume (22.4 L/mol) gives us the number of moles, which can then fuel further calculations, like finding the molar mass of the gas.
This concept is crucial because it allows us to relate the amount of gas (in moles) to the volume it occupies when it's at STP. Knowing the molar volume simplifies gas calculations, especially when determining the number of moles in a given volume.
For example, if we have 0.280 L of a gas at STP, dividing by the molar volume (22.4 L/mol) gives us the number of moles, which can then fuel further calculations, like finding the molar mass of the gas.
Gas Calculations
Calculating properties of gases often involves multiple steps, piecing together several key concepts like the Ideal Gas Law and molar volume. These calculations help determine unknown properties, like the molar mass of a gas.
To calculate molar mass, you need both the mass and the amount of the gas in moles. Using volumes and molar volumes, the moles can be found, after which a simple division gives the molar mass:
\[ M = \frac{m}{n} \]
Here:
To calculate molar mass, you need both the mass and the amount of the gas in moles. Using volumes and molar volumes, the moles can be found, after which a simple division gives the molar mass:
\[ M = \frac{m}{n} \]
Here:
- \(M\) is the molar mass
- \(m\) is the mass in grams
- \(n\) is the number of moles
Other exercises in this chapter
Problem 40
Calculate its volume (in liters) of \(88.4 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) at STP.
View solution Problem 41
A gas at \(772 \mathrm{mmHg}\) and \(35.0^{\circ} \mathrm{C}\) occupies a volume of \(6.85 \mathrm{~L}\). Calculate its volume at STP.
View solution Problem 44
At 741 torr and \(44^{\circ} \mathrm{C}, 7.10 \mathrm{~g}\) of a gas occupy a volume of \(5.40 \mathrm{~L}\). What is the molar mass of the gas?
View solution Problem 45
Ozone molecules in the stratosphere absorb much of the harmful radiation from the sun. Typically, the temperature and pressure of ozone in the stratosphere are
View solution