Four one litre flasks are separately filled with the gases CO2, F2, NH3 and He at the same room temperature and pressure. The ratio of the total number of atoms of these gases present in the different flasks would be?
(1) 1:1:1:1
(2) 1:2:2:3
(3) 3:2:4:1
(4) 2:1:3:2
3:2:4:1
3 as no. Of molecule are same so multiply by no. Of atoms
To determine the ratio of the total number of atoms of gases present in the different flasks, we need to know the molar masses of each gas, as the number of atoms is directly related to the molar mass.
Given that the flasks are filled with CO2, F2, NH3, and He, their respective molar masses are:
CO2: 12 g/mol (C) + 16 g/mol (O) + 16 g/mol (O) = 44 g/mol
F2: 19 g/mol (F) + 19 g/mol (F) = 38 g/mol
NH3: 14 g/mol (N) + 1 g/mol (H) + 1 g/mol (H) + 1 g/mol (H) = 17 g/mol
He: 4 g/mol
Now, we can calculate the number of moles of each gas using their molar masses and the volume (1 liter) at the same room temperature and pressure.
Number of moles = volume (in liters) / molar mass
For CO2: 1 liter / 44 g/mol = 0.0227 moles
For F2: 1 liter / 38 g/mol = 0.0263 moles
For NH3: 1 liter / 17 g/mol = 0.0588 moles
For He: 1 liter / 4 g/mol = 0.25 moles
To find the ratio of the total number of atoms of each gas, we multiply the number of moles by Avogadro's constant (6.022 x 10^23) since one mole of any substance contains Avogadro's number of particles (atoms, molecules, or ions).
Number of atoms = number of moles * Avogadro's constant
For CO2: 0.0227 moles * 6.022 x 10^23 atoms/mole = 1.3666 x 10^22 atoms
For F2: 0.0263 moles * 6.022 x 10^23 atoms/mole = 1.5833 x 10^22 atoms
For NH3: 0.0588 moles * 6.022 x 10^23 atoms/mole = 3.5386 x 10^22 atoms
For He: 0.25 moles * 6.022 x 10^23 atoms/mole = 1.5055 x 10^23 atoms
Now we have the total number of atoms of each gas. To find the ratio, we compare the number of atoms between the gases.
The ratio of the total number of atoms of CO2, F2, NH3, and He is:
1.3666 x 10^22 : 1.5833 x 10^22 : 3.5386 x 10^22 : 1.5055 x 10^23
To simplify the ratio, we can divide each of the values by 1.3666 x 10^22, which is the smallest number in the ratio:
1.3666 x 10^22 / 1.3666 x 10^22 : 1.5833 x 10^22 / 1.3666 x 10^22 : 3.5386 x 10^22 / 1.3666 x 10^22 : 1.5055 x 10^23 / 1.3666 x 10^22
= 1 : 1.1604 : 2.5878 : 11.015
This simplified ratio is not one of the provided answer choices. However, if we round the values to the nearest whole numbers, we get:
1 : 1 : 3 : 11
Thus, the closest answer choice is (3) 3:2:4:1.