Calculate the value of Avogadro's no if density is =2.165g/cm3 find distance bw Na+and Cl_ in NaCl =281pm
To calculate the value of Avogadro's number (symbolized as "N₀"), we'll need to know the density of a substance and the distance between its constituent particles. However, the given information about density and distance is not directly related to Avogadro's number.
Avogadro's number, N₀, is a fundamental constant that represents the number of atoms or molecules in one mole of a substance. It is approximately 6.022 x 10^23 particles per mole.
However, we can use the given information to calculate other quantities.
1. To find the distance between sodium (Na+) and chloride (Cl-) ions in sodium chloride (NaCl), we'll use the given distance of 281 pm (picometers).
2. To convert picometers to centimeters, divide by 10^12 (1 pm = 1 x 10^-12 cm). So, 281 pm = 2.81 x 10^-8 cm.
3. The density of NaCl is given as 2.165 g/cm³.
Now, here's how to calculate the value of Avogadro's number using the given information:
1. Determine the molar mass of NaCl:
The molar mass of Na is approximately 22.99 g/mol, and the molar mass of Cl is approximately 35.45 g/mol. Since NaCl has a one-to-one ratio of Na to Cl, the molar mass of NaCl is 22.99 + 35.45 = 58.44 g/mol.
2. Calculate the volume of one mole of NaCl:
Using the given density (2.165 g/cm³), we can deduce that one mole of NaCl has a mass of 58.44 g (as determined in step 1). Dividing the mass by the density gives us the volume:
volume = mass / density = 58.44 g / 2.165 g/cm³
3. Convert the volume to cubic centimeters:
Since the density is given in grams per cubic centimeter, the volume is already in cubic centimeters.
4. Calculate the number of unit cells in one mole of NaCl:
The volume of one mole of NaCl (from step 3) represents the volume of a certain number of NaCl unit cells. Each unit cell contains one Na+ ion and one Cl- ion. Therefore, the number of unit cells in one mole of NaCl is equal to Avogadro's number (N₀). This means that N₀ is equal to volumetric density (unit cells/cm³) multiplied by the volume of one mole of NaCl.
5. Calculate Avogadro's number:
Multiply the volumetric density by the volume of one mole of NaCl to obtain Avogadro's number:
N₀ = volumetric density (unit cells/cm³) * volume of one mole of NaCl (cm³)
Please note that the calculation provided above is an estimation based on the given information, and the exact value of Avogadro's number is a well-known constant.
For NaCl lattice,
a=2(r++r−)=2×281=562 pm
d=zMNA×V
z is 4 because only 4 NaCl are present in a unit cell
2.165=4×58.5NA×(562×10−10)3
NA=6.01×1023