A cylinder contains hydrogen gas at a pressure of $249 ext{ kPa}$ and temperature $27^\circ ext{C}$. Its de

Question

A cylinder contains hydrogen gas at a pressure of $249 	ext{ kPa}$ and temperature $27^\circ	ext{C}$. Its density is: ($R=8.3 	ext{ J mol}^{-1}	ext{K}^{-1}$)

Accepted Answer

1.  **Identify the Formula:** The density ($ho$) of an ideal gas is given by the relation $ho = \frac{PM}{RT}$, derived from the ideal gas equation $PV = nRT$. 
2.  **Convert Units to SI:** 
    *   Pressure ($P$) = $249 	ext{ kPa} = 249 	imes 10^3 	ext{ Pa}$.
    *   Temperature ($T$) = $27^\circ	ext{C} = 27 + 273 = 300 	ext{ K}$.
    *   Molar Mass ($M$) of Hydrogen ($H_2$) = $2 	ext{ g/mol} = 2 	imes 10^{-3} 	ext{ kg/mol}$.
3.  **Substitute Values:** 
    $ho = \frac{(249 	imes 10^3) 	imes (2 	imes 10^{-3})}{8.3 	imes 300}$
4.  **Calculate:** 
    Denominator: $8.3 	imes 300 = 2490$. 
    Numerator: $249 	imes 2 = 498$. 
    $ho = \frac{498}{2490} = 0.2 	ext{ kg/m}^3$.

Step-by-Step Solution

Practice All PHYSICS Questions