According to the Ideal Gas Equation, $PV = nRT$. Since $n = \frac{m}{M}$ (mass / Molar mass) and density $\rho = \frac{m}{V}$, we can substitute to find the relationship between density and pressure: $P = \frac{m}{V} \frac{RT}{M} = \rho \frac{RT}{M}$ Rearranging for the ratio of density to pressure: $\frac{\rho}{P} = \frac{M}{RT}$ For a fixed mass of a specific gas, the Molar mass ($M$) is constant. Thus, the ratio is inversely proportional to the absolute temperature: $\frac{\rho}{P} \propto \frac{1}{T}$

1. Initial Condition: $T_1 = 10^\circ\text{C} = 10 + 273 = 283 \text{ K}$. $x = \frac{k}{283} \quad \text{(where } k \text{ is a constant)}$
2. Final Condition: $T_2 = 110^\circ\text{C} = 110 + 273 = 383 \text{ K}$. $x' = \frac{k}{383}$
3. Calculate Ratio: $\frac{x'}{x} = \frac{k / 383}{k / 283} = \frac{283}{383}$ $x' = \frac{283}{383}x$