A 300 ml of hydrogen was collected over water at 300 k & the pressure over water was 760torr & vapour pressure of water was 19torr .How many millimoles of water will form??

To determine how many millimoles of water will form when 300 ml of hydrogen gas is collected over water, we need to consider the conditions under which the gas was collected, including the total pressure and the vapor pressure of water. Let's break this down step by step.

Understanding the Gas Laws

When gases are collected over water, the total pressure exerted by the gas mixture is the sum of the partial pressures of the gas and the water vapor. This relationship is described by Dalton's Law of Partial Pressures.

Calculating the Partial Pressure of Hydrogen

The total pressure (P_total) is given as 760 torr, and the vapor pressure of water (P_water) at 300 K is 19 torr. To find the partial pressure of hydrogen (P_H2), we can use the formula:

• P_H2 = P_total - P_water

Substituting the values:

• P_H2 = 760 torr - 19 torr = 741 torr

Using the Ideal Gas Law

Next, we can apply the Ideal Gas Law, which states:

• PV = nRT

Where:

• P = pressure in atm
• V = volume in liters
• n = number of moles
• R = ideal gas constant (0.0821 L·atm/(K·mol))
• T = temperature in Kelvin

First, we need to convert the pressure from torr to atm:

• P_H2 = 741 torr × (1 atm / 760 torr) = 0.975 atm

Next, convert the volume from milliliters to liters:

• V = 300 ml × (1 L / 1000 ml) = 0.300 L

Calculating Moles of Hydrogen

Now we can rearrange the Ideal Gas Law to solve for n (the number of moles of hydrogen):

• n = PV / RT

Substituting the known values:

• n = (0.975 atm) × (0.300 L) / (0.0821 L·atm/(K·mol) × 300 K)

Calculating this gives:

• n ≈ 0.012 moles of H2

Converting Moles to Millimoles

To find the number of millimoles, we multiply by 1000:

• Millimoles of H2 = 0.012 moles × 1000 = 12 mmoles

Water Formation Reaction

In a reaction where hydrogen gas reacts with oxygen to form water, the balanced equation is:

• 2 H2 + O2 → 2 H2O

This indicates that 2 moles of hydrogen produce 2 moles of water. Therefore, the number of moles of water formed will be equal to the number of moles of hydrogen consumed.

Calculating Millimoles of Water

Since we have 0.012 moles of hydrogen, the same amount of moles of water will be produced:

• Millimoles of H2O = 0.012 moles × 1000 = 12 mmoles

Thus, the final answer is that 12 millimoles of water will form from the reaction of the collected hydrogen gas.