What pressure (in atm) is exerted by a column of toluene (C7H8) 87.0 m high? The density of toluene and mercury is is .867 g/cm³ and 13.6 g/cm³ respectively. Express your answer in decimal notation.
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.
![### Calculation of Pressure Exerted by a Toluene Column
#### Problem Statement:
What pressure (in atm) is exerted by a column of toluene (C₇H₈) that is 87.0 meters high? The densities of toluene and mercury are 0.867 g/cm³ and 13.6 g/cm³ respectively. Express your answer in decimal notation.
#### Given:
- Height of the toluene column (h) = 87.0 meters
- Density of toluene (ρ_toluene) = 0.867 g/cm³
- Density of mercury (ρ_mercury) = 13.6 g/cm³
To find the pressure exerted by a column of liquid, the following formula is used:
\[ P = \rho g h \]
Where:
- \( P \) is the pressure,
- \( \rho \) is the density of the liquid,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)),
- \( h \) is the height of the liquid column.
#### Calculation Steps:
1. **Convert the density of toluene from g/cm³ to kg/m³:**
\[ 0.867 \, \frac{g}{cm^3} = 0.867 \times 1000 \, \frac{kg}{m^3} = 867 \, \frac{kg}{m^3} \]
2. **Calculate the pressure exerted by the toluene column:**
\[ P_{\text{toluene}} = (867 \, \frac{kg}{m^3}) \times (9.81 \, \frac{m}{s^2}) \times (87.0 \, m) \]
\[ P_{\text{toluene}} = 740149.29 \, \text{Pa} \]
3. **Convert the pressure from Pascals to atmospheres (1 atm = 101325 Pa):**
\[ P_{\text{toluene}} = \frac{740149.29 \, \text{Pa}}{101325 \, \text{Pa/atm}} \]
\[ P_{\text{toluene}} \approx 7.30 \, \text{atm}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9413ee1b-018f-4e4f-9457-fb88f0adac84%2F9c56624d-e701-4558-9359-22933b93b541%2Ftxqo63a_processed.jpeg&w=3840&q=75)
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
