In a container, 1 g of hydrogen and 1 g of oxygen are taken. Find the ratio of hydrogen pressure to oxygen pressure.
Solution and Explanation
Step 1: Use the ideal gas law.
For an ideal gas: \[ P = \frac{nRT}{V} \] Since \( R, T, V \) are the same for both gases, the ratio of pressures depends only on the ratio of moles: \[ \frac{P_H}{P_O} = \frac{n_H}{n_O} \]
Step 2: Calculate moles of each gas.
For hydrogen (\( H_2 \)): \[ n_H = \frac{\text{mass}}{\text{molar mass}} = \frac{1}{2} = 0.5 \]
For oxygen (\( O_2 \)): \[ n_O = \frac{1}{32} = 0.03125 \]
Step 3: Find the ratio of pressures.
\[ \frac{P_H}{P_O} = \frac{n_H}{n_O} = \frac{0.5}{0.03125} = 16 \]
Final Answer:
\[ \boxed{\frac{P_H}{P_O} = 16} \]
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Concepts Used:
Pressure
Pressure is defined as the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
Everyday examples of pressure are:
- The working of the vacuum cleaner is an example of pressure. The fan inside the vacuum creates a low-pressure region which makes it easy to suck the dust particles inside the vacuum.
- Using a knife for cutting is another example of pressure. The area exposed from the knife is small but the pressure is high enough to cut the vegetables and fruits.
Formula:
When a force of ‘F’ Newton is applied perpendicularly to a surface area ‘A’, then the pressure exerted on the surface by the force is equal to the ratio of F to A. The formula for pressure (P) is:
P = F / A
Units of Pressure:
The SI unit of pressure is the pascal (Pa)
A pascal can be defined as a force of one newton applied over a surface area of a one-meter square.