The values of pressure equilibrium constant recorded at different temperatures for the following equilibrium reaction have been given below
$$A(g) \rightleftharpoons B(g) + C(g)$$

The magnitude of $$\frac{\Delta H^\circ}{R}$$ calculated from the above data is _______. (Nearest integer)

To find the magnitude of $$\ \frac{\triangle\ H^{\circ\ }}{R}$$, we use the integrated form of the van 't Hoff equation:

$$\log_{10}K_p=-\frac{\triangle H^{\circ\ }}{2.303RT}\ +$$ Constant

Step 1: Identify the slope

The equation is in the form of $$y=mx+c$$, 

where:

$$y=\log_{10}K_p$$

$$x=\frac{1}{T}$$

$$m\left(slope\right)=-\frac{\triangle H^{\circ\ }}{2.303R}\ $$

Using the first two points from the table:

$$\left(x_1,y_1\right)=\left(0.05,3.5\right)$$

$$\left(x_2,y_2\right)=\left(0.06,2.5\right)$$

Therefore, 

$$slope\left(m\right)=\frac{y_2-y_1}{x_2-x_1}=\frac{2.5-3.5}{0.06-0.05}=-\frac{0.1}{0.01}=-100$$

Step 2: Calculate $$\ \frac{\triangle\ H^{\circ\ }}{R}$$

Equating the calculated slop $$(m)$$

$$-100=-\frac{\triangle H^{\circ\ }}{2.303R}$$

$$100\times\ 2.303=\frac{\triangle H^{\circ\ }}{R}$$

$$230.3=\frac{\triangle H^{\circ\ }}{R}$$

Therefore, the nearest integer is 230.