Problem 17 - General Chemistry: Principles and Modern Applications

Question

What is the mass of argon gas in a \(75.0 \mathrm{mL}\) volume at STP?

Step-by-Step Solution

Answer

The mass of argon gas in a \(75.0 \mathrm{mL}\) volume at STP is approximately \(0.134 \mathrm{g}\).

Step 1: Convert the volume to liters

To start, convert the volume given in milliliters (mL) to liters (L) because STP conditions are usually expressed in liters. This is done by dividing the volume by 1000 as follows: \(75.0 \mathrm{mL} = 75.0/1000 = 0.075 \mathrm{L}\) .

Step 2: Calculate the number of moles of the gas

Next, use the volume and the molar volume at STP to calculate the number of moles of the gas. The molar volume at STP is typically given as \(22.4 \mathrm{L/mol}\) . Therefore the number of moles can be calculated using the formula \( n = V/V_m = 0.075 \mathrm{L} /22.4 \mathrm{L/mol} = 0.00335 \mathrm{mol}\).

Step 3: Calculate the mass of the gas

Finally, use the number of moles and the molar mass of argon to calculate the mass of the gas. The molar mass of argon is around \(40 g/mol\) . The formula is \( m = n \cdot M = 0.00335 \mathrm{mol} \cdot 40 \mathrm{g/mol} = 0.134 \mathrm{g}\).

Key Concepts

Volume Conversion

When dealing with gas calculations, understanding how to convert between different volume units is essential, especially from milliliters (mL) to liters (L). This is because gases under Standard Temperature and Pressure (STP) conditions are often measured in liters. Volume conversion is straightforward; you simply divide the volume in milliliters by 1000 to get the volume in liters.
For example, if you have a volume of 75.0 mL, converting it to liters involves the simple calculation:

• Divide by 1000:
  \(75.0 \text{ mL} = \frac{75.0}{1000} = 0.075 \text{ L}\).

This step ensures that such volumes align with the commonly used literature and scientific calculations when working with gases at STP.

Molar Volume

The concept of molar volume is fundamental when working with gases. At Standard Temperature and Pressure (STP), which is defined as 0°C (273.15 K) and 1 atm pressure, one mole of any ideal gas occupies the same volume, which is 22.4 liters.
The molar volume makes it possible to calculate the amount of substance (in moles) from a gas's measured volume. If you know the volume of a gas at STP, the relationship can be defined as:

• The formula for finding moles from volume:
  \[ n = \frac{V}{V_m} \]
  where \(n\) is the number of moles, \(V\) is the gas volume, and \(V_m\) is the molar volume (22.4 L/mol at STP).

Understanding molar volume helps in converting between the volume of a gas measured at STP and the number of moles, thereby connecting macroscopic quantities with microscopic chemical identities.

Molar Mass of Argon

Argon, a noble gas, is an element with atomic number 18 and commonly found in the Earth's atmosphere. The molar mass of an element refers to the mass of one mole of its atoms. For argon, the molar mass is roughly 40 g/mol. This value is derived from the atomic mass because each mole contains Avogadro's number of atoms.
To find the mass of a specific quantity of argon, such as in a gas sample, you multiply the number of moles by the molar mass:

• The formula used:
  \[ m = n \times M \]
  where \(m\) is the mass, \(n\) is the number of moles, and \(M\) is the molar mass of argon (40 g/mol).

Knowing the molar mass is crucial for calculating how much argon is in a given set of conditions, thus facilitating various scientific and industrial applications.