To find the density of hydrogen gas in the cylinder, we can use the ideal gas equation and the definition of density.$\\$The ideal gas equation is:$\\ PV = nRT \\$Where:$\\$• $P$ is the pressure in pascals (Pa),$\\$• $V$ is the volume in cubic meters (m$^3$),$\\$• $n$ is the number of moles,$\\$• $R$ is the universal gas constant,$\\$• $T$ is the temperature in kelvin (K).$\\$We also know that:$\\ n = \frac{m}{M} \\$Where:$\\$• $m$ is the mass of the gas,$\\$• $M$ is the molar mass of the gas.$\\$Substituting $n = \frac{m}{M}$ into the ideal gas equation, we get:$\\ PV = \frac{m}{M}RT \\$Rearranging for density $\rho$ (where $\rho = \frac{m}{V}$):$\\ \rho = \frac{PM}{RT} \\$Given:$\\ P = 249$ kPa$= 249000$ Pa$\\ T = 278$ K$\\ R = 8.3$ J mol$^{-1}$ K$^{-1} \\ M = 2$ g/mol$= 0.002$ kg/mol$$ (for hydrogen gas)$\\$Substitute these values into the density equation:$\\ \rho = \frac{249000 \times 0.002}{8.3 \times 278} \\$Calculate the numerator:$\\ 249000 \times 0.002 = 498 \\$Calculate the denominator:$\\ 8.3 \times 278 = 2307.4 \\$Now, calculate the density:$\\ \rho = \frac{498}{2307.4} \\ \rho \approx 0.2157$ kg/m$^3 \\$Rounding to one decimal place, the density is approximately $0.2$ kg/m$^3. \\$Therefore, the correct option is Option 1: $0.2$ kg/m$^3.$