A 1.28 gram sample of an unknown gas is found to occupy a volume of 0.864 L at a pressure of 618 mmHg and a temperature of 31 °C. Assume ideal behavior. The molar mass of the unknown gas is g/mol. Submit Answer Retry Entire Group 9 more group attempts remaining
Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
![### Determining the Molar Mass of an Unknown Gas
In this exercise, you are provided with a sample of an unknown gas. The properties of the gas sample are as follows:
- **Mass:** 1.28 grams
- **Volume:** 0.864 liters
- **Pressure:** 618 mmHg
- **Temperature:** 31°C
Assume that the gas behaves ideally.
To calculate the molar mass of the unknown gas, you can use the Ideal Gas Law equation:
\[ PV = nRT \]
Where:
- \( P \) is pressure in atmospheres (atm)
- \( V \) is volume in liters (L)
- \( n \) is number of moles (mol)
- \( R \) is the ideal gas constant \( 0.0821 \, \text{L·atm/(mol·K)} \)
- \( T \) is temperature in Kelvin (K)
1. Convert the given pressure from mmHg to atm:
\[ 1 \, \text{atm} = 760 \, \text{mmHg} \]
\[ P = \frac{618 \, \text{mmHg}}{760 \, \text{mmHg/atm}} \approx 0.813 \, \text{atm} \]
2. Convert the temperature from Celsius to Kelvin:
\[ T = 31 \, ^\circ\text{C} + 273.15 = 304.15 \, \text{K} \]
3. Substitute the known values into the ideal gas equation to solve for \( n \):
\[ n = \frac{PV}{RT} \]
\[ n = \frac{(0.813 \, \text{atm})(0.864 \, \text{L})}{(0.0821 \, \text{L·atm/(mol·K)})(304.15 \, \text{K})} \approx 0.035 \, \text{mol} \]
4. Calculate the molar mass (M) of the gas by dividing the mass of the sample by the number of moles:
\[ \text{Molar mass} = \frac{1.28 \, \text{g}}{0.035 \, \text{mol}} \approx 36.57 \, \text{g](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb9bc6dc7-2424-4f69-956a-285f3752d785%2F173c1f01-4a3c-4be8-bbda-0315a1d6e3d1%2Fkcdas6t_processed.jpeg&w=3840&q=75)
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