A sample of gas is stored in an manometer, and the mercury column is 61 mmHg lower on the side open to the gas cabinet than the side open to the atmosphere. What is the pressure of the gas if the pressure atmosphere is measured to be 741 mmHg? 8.12 atm 0.89 atm 0.54 atm 1.05 atm
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.
![### Problem Statement
A sample of gas is stored in a manometer, and the mercury column is 61 mmHg lower on the side open to the gas cabinet than the side open to the atmosphere. What is the pressure of the gas if the pressure atmosphere is measured to be 741 mmHg?
### Multiple Choice Answers
- ⃝ 8.12 atm
- ⃝ 0.89 atm
- ⃝ 0.54 atm
- ⃝ 1.05 atm
### Explanation
The problem involves a manometer, which is used to measure the pressure of a gas. The mercury column difference and the atmospheric pressure are given to calculate the gas pressure.
Given:
- Atmospheric pressure = 741 mmHg
- Difference in mercury column = 61 mmHg
**To find:** Pressure of the gas in atm.
### Solution
1. **Identify Pressure Difference:**
Since the mercury column is lower on the gas side, the gas pressure is higher by 61 mmHg compared to the atmospheric pressure.
2. **Calculate Gas Pressure in mmHg:**
\[
\text{Gas Pressure} = \text{Atmospheric Pressure} + \Delta h
\]
\[
\text{Gas Pressure} = 741 \, \text{mmHg} + 61 \, \text{mmHg} = 802 \, \text{mmHg}
\]
3. **Convert mmHg to atm:**
Use the conversion factor: \(1 \, \text{atm} = 760 \, \text{mmHg} \).
\[
\text{Gas Pressure in atm} = \frac{802 \, \text{mmHg}}{760 \, \text{mmHg/atm}} \approx 1.055 \, \text{atm}
\]
4. **Match with Closest Answer:**
The closest answer to 1.055 atm is 1.05 atm.
### Correct Answer
- ⃝ 1.05 atm](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb077f2ab-172b-438d-8d7b-87f013063300%2F5f177df1-6b8a-4df4-b9e1-6a673a0190b9%2Fz5zv1dw_processed.jpeg&w=3840&q=75)
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