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Four one litre flasks are separately fil...

Four one litre flasks are separately filled with the gases, `O_(2),F_(2),CH_(4)` and `CO_(2)` under the same conditions. The ratio of number of molecules its these gases:

A

`2 : 2 : 4 : 3`

B

`1 : 1 : 1 : 1`

C

`1 : 2 : 3 : 4`

D

`2 : 2 : 3 : 4`

Text Solution

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The correct Answer is:
To solve the problem of finding the ratio of the number of molecules of the gases \( O_2, F_2, CH_4, \) and \( CO_2 \) in one-liter flasks under the same conditions, we can follow these steps: ### Step-by-Step Solution: 1. **Understand Avogadro's Law**: Avogadro's Law states that at the same temperature and pressure, equal volumes of gases contain an equal number of molecules. Since all four flasks are filled with one liter of gas under the same conditions, we can use this law. 2. **Identify the Gases**: The gases in question are \( O_2 \) (oxygen), \( F_2 \) (fluorine), \( CH_4 \) (methane), and \( CO_2 \) (carbon dioxide). 3. **Set Up the Ratio**: Since the volume of each gas is the same (1 liter) and the conditions (temperature and pressure) are the same, we can conclude that the number of moles of each gas will be the same. 4. **Calculate the Number of Molecules**: The number of molecules in a gas can be calculated using the formula: \[ \text{Number of molecules} = \text{Number of moles} \times N_A \] where \( N_A \) is Avogadro's number (\( 6.022 \times 10^{23} \) molecules/mol). However, since the number of moles is the same for all gases, we can express the number of molecules as: \[ N_{O_2} = N_{F_2} = N_{CH_4} = N_{CO_2} \] 5. **Conclude the Ratio**: Therefore, the ratio of the number of molecules of \( O_2, F_2, CH_4, \) and \( CO_2 \) is: \[ 1 : 1 : 1 : 1 \] ### Final Answer: The ratio of the number of molecules of \( O_2, F_2, CH_4, \) and \( CO_2 \) is \( 1 : 1 : 1 : 1 \).
To solve the problem of finding the ratio of the number of molecules of the gases \( O_2, F_2, CH_4, \) and \( CO_2 \) in one-liter flasks under the same conditions, we can follow these steps: ### Step-by-Step Solution: 1. **Understand Avogadro's Law**: Avogadro's Law states that at the same temperature and pressure, equal volumes of gases contain an equal number of molecules. Since all four flasks are filled with one liter of gas under the same conditions, we can use this law. 2. **Identify the Gases**: The gases in question are \( O_2 \) (oxygen), \( F_2 \) (fluorine), \( CH_4 \) (methane), and \( CO_2 \) (carbon dioxide). ...
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