In a research experiment, Marie Curie is trying to invent a new compound which will have 30% concentration of nitrogen by mixing two mixtures of nitrogen, hydrogen and oxygen in the ratio 5:3. The ratio of these gases in the first mixture is 4:5:1 and in the second mixture is 5:7:3. Having found that the resultant concentration of nitrogen in the mixture is not 30%, she dilutes it with more oxygen to make it 30%. Find the ratio of the original mixture to the oxygen which was used for dilution?
Answers
Answer:
1:4 is the correct answer.
Given:
The ratio of hydrogen and oxygen=5:3
The ratio of these gases in 1st mix.= 4:5:1
The ratio of these gases in 2nd mix.=5:7:3
To Find:
The ratio of the original mix. to the oxygen which was used for dilution.
Solution:
- The ratio of the original mix.= 4:5:1+5:7:3
⇒10:12:4
On simplifying, we get
⇒5:3:1
As we know that nitrogen is not 30% in the original solution, so we will calculate what will be the 30% of the nitrogen in the solution-
- Total parts of solution=5+3+1=9
Let 30% of the nitrogen gas be 'x.
- x=(30×9)÷100
By using BODMAS we will solve this equation,
⇒x=270÷100
⇒x=2.7
Now,
- For 5 parts of Nitrogen, the mixture has 1 part of oxygen.
- For 1 part of Nitrogen, the mixture will have (1÷5) parts of oxygen.
- ∴For 2.7 parts of Nitrogen, the mixture will have-
⇒ 2.7×(1÷5) parts of oxygen
⇒0.54 parts of oxygen≈ 0.5 parts of oxygen.
∴The ratio of the original mix. to the oxygen which was used for dilution= ⇒(1÷0.5)
⇒10÷5
⇒2:1
Hence, the ratio of the original mixture to the oxygen which was used for dilution is 2:1.