The pressure exerted by $6.0 \, g$ of methane gas in a $0.03\, m^3$ vessel at $129^{\circ}C$ is (Atomic masses : $C = 12.01, H = 1.01 $ and $R = 8.314 \, JK^{-1} mol^{-1}$)
- 13409 Pa
- 41648 Pa
- 31684 Pa
- 215216 Pa
The Correct Option is B
Solution and Explanation
$T = 129 + 273 = 402$
$K$ mass of methane,
$w = 6.0\, g\, mol.$ mass of methane,
$M=12.01+4\times 1.01=16.05$
From, ideal gas equation,
$pV=nRT$
$p=\frac{6}{16.05}\times \frac{8.314\times 402}{0.03} = 41648Pa$
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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.