Data:
V (volume) = 500.0 mL = 0.5 L
T (temperature) = 15.00ºC
(converting in Kelvin) → TK = TC + 273 → TK = 15 + 273 = 288 K
P (pressure) = 736.0 mmHg
R (constant) = 62.363 (mmHg*L/mol*K)
m (mass) = 2.688 g
M (Molar Mass) = ? (g/mol)
Formula: General Gas Equation
[tex]P*V = n*R*T \to \boxed{P*V = \frac{m}{M} *R*T}[/tex]
Solving:
[tex]P*V = \frac{m}{M} *R*T[/tex]
[tex]736*0.5 = \frac{2.688}{M} *62.363*288[/tex]
[tex]368 = \frac{2.688}{M} *17960.544[/tex]
Product of extremes equals product of means:
[tex]368*M = 2.688*17960.544[/tex]
[tex]368M = 48277.94227[/tex]
[tex]M = \frac{48277.94227}{368} [/tex]
[tex]M = 131.1900605\to \boxed{\boxed{M \approx 131.2\:g/mol}}[/tex]
Therefore: The gas found to have such a molar mass is xenon gas
