The data obtained from an air sample analysis of an old working in a coal mine are given. O2 17.15%, CO2 3.40%, CH4 2.20%, and N2 77.25%. Considering atmospheric air contains O2 20... The data obtained from an air sample analysis of an old working in a coal mine are given. O2 17.15%, CO2 3.40%, CH4 2.20%, and N2 77.25%. Considering atmospheric air contains O2 20.95%, CO2 0.03%, and N2 79.02%. The percentage of blackdamp in the old working is __ (round off up to 2 decimals).
Understand the Problem
The question is asking to calculate the percentage of blackdamp in an old coal mine working, based on the provided air sample analysis data of different gas concentrations. The user is instructed to round off the answer to two decimals.
Answer
$8.94\%$
Answer for screen readers
The percentage of blackdamp in the old working is $8.94%$.
Steps to Solve
- Identify the components in the old working and the atmosphere
The gases present in the old coal mine are:
- O2: 17.15%
- CO2: 3.40%
- CH4: 2.20%
- N2: 77.25%
The gases in the atmosphere are:
- O2: 20.95%
- CO2: 0.03%
- N2: 79.02%
- Calculate the total gas percentages in the mine
Add the percentages of the gases present in the old working: $$ \text{Total gas in mine} = 17.15 + 3.40 + 2.20 + 77.25 = 100% $$
- Calculate the missing gas percentage in the mine
Blackdamp is typically associated with the absence of oxygen and includes other gases, such as methane (CH4) or carbon dioxide (CO2) in dangerous concentrations. We will find the percentage of blackdamp by calculating the difference between atmospheric air and the amount of measurable gases.
Blackdamp percentage is calculated as follows: $$ \text{Blackdamp} = 100% - \text{(concentration of detectable gases)} $$
- Subtract the measured gas concentrations from atmospheric levels
To find the blackdamp percentage:
- Concentrations of each gas in the atmosphere need to be considered first, but in this scenario, we mainly deal with the lack of O2.
Calculating blackdamp: $$ \text{Blackdamp} = (20.95 - 17.15) + (0.03 - 3.40) + (79.02 - 77.25) $$
This gives:
- The loss of O2: $20.95 - 17.15 = 3.80%$
- The excess CO2: $3.40 - 0.03 = 3.37%$
- The negligible N2 difference: $79.02 - 77.25 = 1.77%$
- Sum everything up to find the blackdamp percentage
$$ \text{Total Blackdamp} = 3.80 + 3.37 + 1.77 $$
Now, let's calculate that:
$$ \text{Total Blackdamp} = 3.80 + 3.37 + 1.77 = 8.94% $$
- Round off to two decimals
The final step is to round the calculated percentage to two decimal places which remains 8.94%.
The percentage of blackdamp in the old working is $8.94%$.
More Information
Blackdamp generally refers to a mixture of gases present in coal mines, particularly those harmful or hazardous to health due to low oxygen levels. It can contain carbon dioxide and methane in varying percentages.
Tips
- Not considering all relevant gases when calculating the blackdamp percentage. Ensure to assess the surrounding atmospheric conditions accurately.
- Forgetting to round off the final answer correctly according to the question requirements.
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