At $30^{\circ}C$, the amounts of acetone adsorbed at partial pressures of $10$ and $100\:mmHg$ are $0.1$ and $0.4\:kg$ acetone/$kg$ activated carbon, respectively. Assume Langmuir isotherm described the adsorption of acetone on activated carbon. What is the amount of acetone adsorbed (in $kg$ per $kg$ of activated carbon) at a partial pressure of $50\:mmHg$ and $30^{\circ}C$?

1. $0.23$
2. $0.25$
3. $0.30$
4. $0.35$