Solid white P melts then vaporizes at high temperatures. Gaseous white P effuses at a rate that is 0.404 times that of neon in the same apparatus under the same conditions. How many atoms are in a molecule of gaseous white phosphorus?
.404 = sqrt (atomicmassNe/molcmassPx)
solve for the molemass of P
then, number atoms=molemassP/atomicmassP
sdfg
To find the number of atoms in a molecule of gaseous white phosphorus, we need to use the concept of effusion rates and the ratio of the molecular masses.
1. Start by understanding the concept of effusion. Effusion is the escape of gas molecules through a tiny hole or opening. According to Graham's law of effusion, the rate of effusion of a gas is inversely proportional to the square root of its molar mass.
2. We are given that the effusion rate of gaseous white P is 0.404 times that of neon in the same apparatus under the same conditions.
3. The molar mass of neon (Ne) is 20.18 g/mol.
4. Let's assume that gaseous white phosphorus (P) has a molar mass of M g/mol.
5. Using Graham's law of effusion, we can set up the following ratio:
(Rate of effusion of white P) / (Rate of effusion of Ne) = sqrt(M Ne) / sqrt(M P)
Since the rate of effusion of white P is 0.404 times that of Ne, the ratio becomes:
0.404 = sqrt(M Ne) / sqrt(M P)
6. Square both sides of the equation to eliminate the square roots:
(0.404)^2 = (sqrt(M Ne) / sqrt(M P))^2
0.163216 = (M Ne) / (M P)
7. Cross multiply and simplify:
0.163216 * M P = M Ne
M P = M Ne / 0.163216
8. Substitute the molar mass values:
M P = 20.18 g/mol / 0.163216
9. Calculate M P:
M P ≈ 123.595 g/mol
10. The molar mass of white phosphorus (P4) is approximately 123.595 g/mol.
11. Since each molecule of white phosphorus contains 4 phosphorus atoms (P4), to find the number of atoms in a molecule of gaseous white phosphorus, we multiply the molar mass by the Avogadro's number (6.022 x 10^23 atoms/mol).
Number of atoms in a molecule of gaseous white phosphorus = 4 x (6.022 x 10^23 atoms/mol)
Number of atoms in a molecule of gaseous white phosphorus ≈ 2.4088 x 10^24 atoms.
To determine the number of atoms in a molecule of gaseous white phosphorus, we need to use the concept of effusion rates and Avogadro's law.
Effusion is the process by which a gas escapes through a tiny hole into a vacuum. According to Graham's law of effusion, the rate of effusion of a gas is inversely proportional to the square root of its molar mass. In other words, lighter molecules effuse faster than heavier ones.
We are given that the effusion rate of gaseous white phosphorus (P) is 0.404 times that of neon (Ne) under the same conditions. So, we can set up the following proportion:
(Number of moles of P / Molar mass of P) = (Number of moles of Ne / Molar mass of Ne)
Let's assume that we have 1 mole of Ne (since the molar mass of Ne is 20.18 g/mol), and we'll find the molar mass of P.
Now we have:
(Number of moles of P / Molar mass of P) = (1 mole of Ne / 20.18 g/mol)
Rearranging the equation to solve for the molar mass of P:
Molar mass of P = (Number of moles of P / (1 mole of Ne / 20.18 g/mol))
Given that the effusion rate of P is 0.404 times that of Ne, we can set up another proportion:
(Effusion rate of P / Effusion rate of Ne) = (Square root of the molar mass of Ne / Square root of the molar mass of P)
And we know that the effusion rate of P is 0.404 times the effusion rate of Ne:
0.404 = (Square root of the molar mass of Ne / Square root of the molar mass of P)
Squaring both sides of the equation:
0.163216 = (molar mass of Ne / molar mass of P)
Rearranging the equation to solve for the molar mass of P:
molar mass of P = molar mass of Ne / 0.163216
Substituting the molar mass of Ne (20.18 g/mol) into the equation:
molar mass of P = 20.18 g/mol / 0.163216
molar mass of P = 123.74 g/mol
Finally, we can calculate the number of atoms in a molecule of gaseous white phosphorus using Avogadro's number, which states that 1 mole of any substance contains 6.022 x 10^23 entities (atoms, molecules, ions, etc.). Since we now have the molar mass of P, we can calculate the number of atoms:
Number of atoms in a molecule of P = (6.022 x 10^23 atoms/mol) / (molar mass of P)
Substituting the molar mass of P (123.74 g/mol) into the equation:
Number of atoms in a molecule of P = (6.022 x 10^23 atoms/mol) / (123.74 g/mol)
Evaluating the expression:
Number of atoms in a molecule of P ≈ 4.867 x 10^21 atoms
Therefore, there are approximately 4.867 x 10^21 atoms in a molecule of gaseous white phosphorus.