At 400 K, the following graph is obtained for \( x \) moles of an ideal gas. \( x \) is equal to (R = gas constant, P = pressure, V = volume)
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For ideal gases, \( PV = nRT \) is the equation of state. The slope of the P vs. \( 1/V \) graph gives the relationship between the pressure, temperature, and volume at constant temperature.
The equation of the graph at constant temperature for an ideal gas follows Boyle's law, which is:
\[
PV = nRT
\]
Given the graph, it suggests a straight-line relation between pressure and the inverse of volume, which implies that the slope \( m \) of the line is related to the equation. The correct relation would be:
\[
m = \frac{1}{400R}
\]
Thus, the slope is \( \frac{m}{400R} \).
