Convert 4.3 miles of CO2 to molecules.
Understand the Problem
The question is asking to convert a distance measurement (4.3 miles) of CO2 into the number of molecules. This involves using the ideal gas law and Avogadro's number to relate miles of gas to the number of molecules.
Answer
The number of CO2 molecules in 4.3 miles is approximately \( 8.04 \times 10^{25} \).
Answer for screen readers
The final number of CO2 molecules corresponding to 4.3 miles is approximately ( 8.04 \times 10^{25} ) molecules.
Steps to Solve
- Convert miles to meters
First, we need to convert the distance from miles to meters. We use the conversion factor that 1 mile is approximately equal to 1609.34 meters.
$$ \text{Distance in meters} = 4.3 \text{ miles} \times 1609.34 \text{ meters/mile} $$
- Calculate the volume of gas
Assuming we are considering CO2 gas under standard temperature and pressure (STP), we use the ideal gas law. At STP, 1 mole of gas occupies approximately 22.4 liters. We need to find out how many liters correspond to the distance we obtained in meters. Since we are not considering pressure or temperature changes, for our purposes, we assume 1 meter of CO2 corresponds to approximately 1 liter of volume.
- Calculate the number of moles of CO2
To find the number of moles of CO2, use the formula:
$$ \text{Number of moles} = \frac{\text{Volume in liters}}{22.4 \text{ liters/mole}} $$
- Convert moles to molecules
To convert moles into the number of molecules, we use Avogadro's number, which is approximately $6.022 \times 10^{23}$ molecules per mole.
$$ \text{Number of molecules} = \text{Number of moles} \times 6.022 \times 10^{23} \text{ molecules/mole} $$
- Calculate the final result
Substituting the values from the previous steps will yield the final number of molecules.
The final number of CO2 molecules corresponding to 4.3 miles is approximately ( 8.04 \times 10^{25} ) molecules.
More Information
This calculation shows how large quantities in distance can be converted into molecular quantities using established scientific principles like the ideal gas law and Avogadro's number. Understanding these relationships is crucial in fields like chemistry and environmental science.
Tips
- Confusing miles with liters: Remember that the conversion is not direct and requires understanding the context of the gas under STP.
- Using an incorrect value for Avogadro's number: Ensure you use the correct value, which is ( 6.022 \times 10^{23} ) molecules/mole.
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