A mixture of CO and CO2 having a volume of 20 ml is mixed with x ml of oxygen and electrically sparked. The volume after explosion is (16 + x)ml under the same conditions. What would be the residue volume if 30 ml of the original mixture is treated with aqueous NaOH? (a) 12 ml (b) 10 ml (c) 9 ml (d) 8 ml

To find the residue volume after treating the mixture with aqueous NaOH, we need to first understand the chemical reaction that occurs when CO and CO2 react with NaOH.

When CO reacts with NaOH, it forms sodium formate (HCOONa) and water:

CO + NaOH -> HCOONa + H2O

When CO2 reacts with NaOH, it forms sodium carbonate (Na2CO3) and water:

CO2 + 2NaOH -> Na2CO3 + H2O

Since we have a mixture of CO and CO2, both reactions will occur simultaneously.

Now, let's calculate the residue volume.

We are given that the original mixture has a volume of 20 ml. After the explosion, the volume is (16 + x) ml.

Since both CO and CO2 will react, we need to determine the volume of oxygen (x ml) required for complete reaction.

First, we calculate the volume of CO and CO2 in the original mixture:

Volume of CO = 20 ml * (fraction of CO in the mixture)
Volume of CO2 = 20 ml * (fraction of CO2 in the mixture)

Let's assume that the fraction of CO in the mixture is a and the fraction of CO2 is b.

So, we have:
Volume of CO = 20 ml * a
Volume of CO2 = 20 ml * b

Since the total volume of the mixture is 20 ml, we can write:
a + b = 1

Next, we need to calculate the volume of oxygen required for complete reaction.

For CO:
1 mole of CO reacts with 1 mole of NaOH.
So, the volume of oxygen required to react with CO = Volume of CO = 20 ml * a

For CO2:
1 mole of CO2 reacts with 2 moles of NaOH.
So, the volume of oxygen required to react with CO2 = Volume of CO2 * 2 = 20 ml * b * 2

Therefore, the total volume of oxygen required (x ml) will be:
x = Volume of CO + Volume of CO2 * 2
x = 20 ml * a + 20 ml * b * 2

Now, let's calculate the residue volume after reacting 30 ml of the original mixture with aqueous NaOH.

The total volume of the mixture is given as 30 ml.

First, we calculate the volume of CO and CO2 in the 30 ml of the mixture:

Volume of CO in 30 ml = 30 ml * (fraction of CO in the mixture) = 30 ml * a
Volume of CO2 in 30 ml = 30 ml * (fraction of CO2 in the mixture) = 30 ml * b

Now, we calculate the volume of NaOH required to react with CO and CO2:

For CO:
1 mole of CO reacts with 1 mole of NaOH.
So, the volume of NaOH required to react with CO = Volume of CO = 30 ml * a

For CO2:
1 mole of CO2 reacts with 2 moles of NaOH.
So, the volume of NaOH required to react with CO2 = Volume of CO2 * 2 = 30 ml * b * 2

Therefore, the total volume of NaOH required will be:
Volume of NaOH = Volume of CO + Volume of CO2 * 2
Volume of NaOH = 30 ml * a + 30 ml * b * 2

Finally, to find the residue volume after reaction with NaOH, we subtract the volume of NaOH used from the total volume of the mixture:

Residue volume = Total volume of the mixture - Volume of NaOH
Residue volume = 30 ml - (30 ml * a + 30 ml * b * 2)

To determine the specific residue volume, you will need to know the values of fractions a and b, which are not provided in the question. Once you have those values, substitute them into the equation and calculate the residue volume.

Unfortunately, without the values of fractions a and b, we cannot give you a definitive answer.

To solve this problem, we need to understand the reaction happening during the explosion and the reaction happening when the original mixture is treated with aqueous NaOH.

Let's break down the information given step by step:

1. A mixture of CO and CO2 with a volume of 20 ml is mixed with x ml of oxygen.
2. The mixture is electrically sparked, causing an explosion.
3. The volume after the explosion is (16 + x) ml under the same conditions.
4. 30 ml of the original mixture is treated with aqueous NaOH.

Now let's solve the problem step by step:

Step 1: Find the initial volume of CO and CO2 (20 ml).

Step 2: Determine the volume of oxygen added (x ml).

Step 3: Calculate the total volume after the explosion.
The total volume before the explosion is 20 ml (CO and CO2). We add x ml of oxygen, so the total initial volume is 20 + x ml. After the explosion, the volume is reduced to (16 + x) ml. We can express this as:
20 + x - (volume lost during the explosion) = 16 + x ml

Since the volume of CO and CO2 is reduced during the explosion, we can assume it has reacted with something else. Let's call the volume reacted during the explosion "y ml". The equation becomes:
20 + x - y = 16 + x

Step 4: Determine the volume of CO and CO2 remaining after the explosion (residue volume).
The residue volume is the volume that was not reacted during the explosion, which is the original volume minus the volume reacted (y ml).
Residue volume = 20 - y ml.

Step 5: Calculate the volume of CO and CO2 reacted with aqueous NaOH.
From Step 4, we know that the residue volume after the explosion is 20 - y ml. However, only 30 ml of the original mixture is treated with aqueous NaOH. So we need to find the volume of CO and CO2 in the 30 ml treated with NaOH.
The volume reacted with NaOH = (30/20) * (20 - y)
= 30 - (3/2)y.

Step 6: Find the residue volume after treating with NaOH.
The residue volume after treating with NaOH is equal to the residue volume after the explosion minus the volume reacted with NaOH.
Residue volume = (20 - y) - (30 - (3/2)y)
= 20 - y - 30 + (3/2)y
= (1/2)y - 10.

Finally, to find the residue volume, we can substitute different values of y into this equation and check which option matches the result. Options (a) 12 ml, (b) 10 ml, (c) 9 ml, (d) 8 ml.

Note: The value of y will depend on the reaction occurring during the explosion, and this information is not provided in the question.

I may have missed something but I don't think this problem has been posted correctly. If I start with 20 mL CO and no mL CO2 it will form 20 mL CO2. If I start with no CO and 20 mL CO2 it will have 20 mL CO2 after the spark. I don't see how you can get less than 20 if you start with a mixture with a total of 20.