States of Matter

The slope of an isochore (a line where volume does not change) for an ideal gas is given by $\frac{dp}{dT} = \frac{nR}{V}$, where:$n =$ number of moles,$R =$ gas constant,$V =$ volume.Here, the slope is $0.082 \text{atm} \text{K}^{-1}, n=1$, and $R=0.082 \text{L} \text{atm} \text{mol}^{-1} \text{K}^{-1}$.Substitute the known values into the formula:$0.082 = \;\frac{1 \times 0.082}{V}$Solve for $V$ :$V = 1 \text{L}$Now, use the ideal gas equation: $p V = n R T$.Substitute the values: $p \times 1 = 1 \times 0.082 \times 12.2$Calculate the multiplication: $0.082 \times 12.2 = 1.0004$So, $p = 1.0004 \text{atm}$. Round to nearest whole number: $p = 1 \text{atm}$