when 0.02litre of a mixture of hydrogen and oxygen was exploded,0.003litre of oxygen remained.calculate the initial composition of the mixture in per cent by volume

To determine the initial composition of the mixture of hydrogen and oxygen, we can use the information provided about the volumes before and after the explosion. Let's break down the problem step by step.

Understanding the Reaction

When hydrogen (H₂) reacts with oxygen (O₂), they undergo a chemical reaction to form water (H₂O). The balanced equation for this reaction is:

• 2 H₂ + O₂ → 2 H₂O

This equation tells us that two volumes of hydrogen react with one volume of oxygen. Therefore, for every 1 volume of oxygen consumed, 2 volumes of hydrogen are needed.

Initial and Final Volumes

We start with a total volume of 0.02 liters of the gas mixture. After the explosion, we are left with 0.003 liters of oxygen. This means that:

• Initial volume of the mixture = 0.02 liters
• Remaining volume of oxygen after the reaction = 0.003 liters

To find out how much oxygen was consumed, we subtract the remaining volume from the initial volume of oxygen:

• Volume of oxygen consumed = Initial volume of oxygen - Remaining volume of oxygen

Calculating the Volume of Oxygen Consumed

Let’s denote the initial volume of oxygen in the mixture as \( V_O \) and the initial volume of hydrogen as \( V_H \). We know that:

• V_O + V_H = 0.02 liters
• V_O - 0.003 = Volume of oxygen consumed

From the reaction, we know that for every 1 volume of oxygen consumed, 2 volumes of hydrogen are needed. Therefore, if we denote the volume of oxygen consumed as \( V_{O_{consumed}} \), we can express the volume of hydrogen consumed as:

• V_{H_{consumed}} = 2 \times V_{O_{consumed}}

Setting Up the Equations

Now, we can express the consumed volumes in terms of \( V_O \):

• Volume of oxygen consumed = \( V_O - 0.003 \)
• Volume of hydrogen consumed = \( 2 \times (V_O - 0.003) \)

Since the total initial volume of the mixture is 0.02 liters, we can set up the equation:

• V_H + (V_O - 0.003) + 2 \times (V_O - 0.003) = 0.02

Solving the Equations

Substituting \( V_H \) from the first equation into the second gives:

• V_H = 0.02 - V_O

Now, substituting this into the total volume equation:

• (0.02 - V_O) + (V_O - 0.003) + 2 \times (V_O - 0.003) = 0.02

Simplifying this equation:

• 0.02 - V_O + V_O - 0.003 + 2V_O - 0.006 = 0.02
• 0.02 - 0.009 + 2V_O = 0.02
• 2V_O = 0.02 - 0.011
• 2V_O = 0.009
• V_O = 0.0045 liters

Finding the Volume of Hydrogen

Now that we have \( V_O \), we can find \( V_H \):

• V_H = 0.02 - 0.0045 = 0.0155 liters

Calculating the Percent Composition

To find the percentage composition by volume of each gas in the mixture, we use the formula:

• Percentage of gas = (Volume of gas / Total volume) × 100

Calculating for oxygen:

• Percentage of O₂ = (0.0045 / 0.02) × 100 = 22.5%

Calculating for hydrogen:

• Percentage of H₂ = (0.0155 / 0.02) × 100 = 77.5%

Final Composition

Thus, the initial composition of the mixture is:

• Oxygen (O₂): 22.5%
• Hydrogen (H₂): 77.5%

This analysis shows how we can systematically approach a problem involving gas reactions and volume calculations, leading us to understand the initial composition of the mixture. If you have any further questions about this topic or related concepts, feel free to ask!