Question

A graph plotted between logV and logT for 2 mol of gas at constant pressure of 0.0821 atm. V and T are in L and K. Which of the following statements are correct?
I. The curve is a straight line with slope -1.
II. The curve is a straight line with slope +1.
III. The intercept on the Y-axis is equal to 2.
IV. The intercept on the Y-axis is equal to 0.3010.
A. I, II
B. III, IV
C. II, IV
D. I, III

Answer 1

Hint: Ideal gas law is also called the general gas equation is the equation of state of a hypothetical or ideal gas. It is a good approximation of the behaviour of many gases under certain conditions.

Complete answer: Let us understand the term; Ideal gas equation is a combination of Boyles’s law, Charles’ law, Avogadro’s law and Gay-Lussac’s law. The ideal gas law is written as: $\text{PV=nRT}$; where $\text{P,V,T and n}$are pressure, volume, moles and temperature.
Let us get back to the question, $\text{P}$ and n are given as 0.0821 atm and 2 mol. Except for pressure, R and n, other quantities are variable. The graph needs to be plotted in between the variable quantities only.
- First put the values given the ideal gas equation, $0.0821\times \text{V=2}\times 0.0821\times \text{T}$; the term 0.0821 is cancelled with each other, the equation is now,$\text{V=2T}$.
Now, apply the log to the equation, the equation is now formulated to $\text{log V = log2}+\text{ logT}$($\text{log2 = 0}\text{.3010}$).
The equation now becomes$\text{log V = 0}\text{.3010}+\text{log T}$; this equation is of the form y = mx+c.
On comparing the two equations, $\text{y =log V}$,$\text{x= log T}$,$\text{m =1 (constant)}$ and $\text{c= 0}\text{.3010}$.
The graph will look something like this,

The graph is a straight line with slope or m equal to +1 and the intercept on y-axis or c is equal to 0.3010. Hence, the correct answer to this question is option ‘c’ (II, IV).
So, the correct answer is “Option C”.

Note: The variables that need to be put in as x and y axis. In the equation, $\text{log V = 0}\text{.3010}+\text{log T}$, log V is in y-axis and log T is in x-axis; the value of slope will be +1 and if log V is in x-axis and log T is in y-axis; the value of slope will be -1. So, the terms on the x and y axis should be specified and known clearly.