A 10-L vessel filled with `O_(2)` at 300 K is connected to an open limb manometer containing glycerine. The level in the open limb was found to be higher than the other limb by 50 cm. Calculate the number of moles of the gas in the vessel (Given `d_("glycerine")=2.72 g mL^(-1), d_(Hg)=13.6 g mL^(-1)`)

Explanation

To solve the problem of calculating the number of moles of oxygen gas in a 10-L vessel at 300 K, we will follow these steps:

### Step 1: Understand the Manometer Setup
The manometer is used to measure the pressure of the gas in the vessel. Since the level of glycerine in the open limb is higher than in the limb connected to the gas, we know that the pressure of the gas is greater than atmospheric pressure.

### Step 2: Calculate the Pressure Difference
We need to convert the height difference of 50 cm of glycerine into pressure. The pressure can be calculated using the formula:
\[ P = h \cdot d \cdot g \]
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