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A mole is a collection of 6.022 xx 10^23...

A mole is a collection of `6.022 xx 10^23` particles and the number `6.022 xx 10^23` is called Avogadro number. The mass of this number of atoms in an element is equal to its gram atomic mass and mass of this number of molecules in a compound is equal to its gram molecular mass. The volume occupied by this number of molecules of a gas at N.T.P is 22.4 L. When `6.022 xx 10^23` molecules of a substance are dissolved in 1L of solution, the solution is known as 1 molar volume.
One million atoms of silver (at. mass = 107.81) atoms weigh

A

`1.79 xx 10^(-16)` g

B

`3.58 xx 10^(-16)` g

C

`3.58 xx 10^(6)` g

D

`5.32 xx 10^(3)` g

Text Solution

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The correct Answer is:
To find the weight of one million atoms of silver, we can follow these steps: ### Step 1: Understand the given data We know that: - The atomic mass of silver (Ag) = 107.81 g/mol - Avogadro's number = \(6.022 \times 10^{23}\) atoms/mol ### Step 2: Calculate the weight of one atom of silver To find the weight of one atom of silver, we use the formula: \[ \text{Weight of one atom} = \frac{\text{Atomic mass}}{\text{Avogadro's number}} \] Substituting the values: \[ \text{Weight of one atom} = \frac{107.81 \text{ g/mol}}{6.022 \times 10^{23} \text{ atoms/mol}} \] ### Step 3: Perform the calculation Calculating the weight of one atom: \[ \text{Weight of one atom} = \frac{107.81}{6.022 \times 10^{23}} \approx 1.79 \times 10^{-22} \text{ g} \] ### Step 4: Calculate the weight of one million atoms Now, to find the weight of one million atoms (which is \(10^6\) atoms), we multiply the weight of one atom by \(10^6\): \[ \text{Weight of 1 million atoms} = \text{Weight of one atom} \times 10^6 \] Substituting the value we calculated: \[ \text{Weight of 1 million atoms} = 1.79 \times 10^{-22} \text{ g} \times 10^6 \] ### Step 5: Perform the final calculation Calculating the weight of one million atoms: \[ \text{Weight of 1 million atoms} = 1.79 \times 10^{-16} \text{ g} \] ### Final Answer The weight of one million atoms of silver is approximately \(1.79 \times 10^{-16}\) grams. ---
To find the weight of one million atoms of silver, we can follow these steps: ### Step 1: Understand the given data We know that: - The atomic mass of silver (Ag) = 107.81 g/mol - Avogadro's number = \(6.022 \times 10^{23}\) atoms/mol ### Step 2: Calculate the weight of one atom of silver ...
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Knowledge Check

  • A mole is a collection of 6.022 xx 10^23 particles and the number 6.022 xx 10^23 is called Avogadro number. The mass of this number of atoms in an element is equal to its gram atomic mass and mass of this number of molecules in a compound is equal to its gram molecular mass. The volume occupied by this number of molecules of a gas at N.T.P is 22.4 L. When 6.022 xx 10^23 molecules of a substance are dissolved in 1L of solution, the solution is known as 1 molar volume. The mass of 10 molecules of naphthalene (C_(10)H_(8))

    A
    `2.12 xx 10^(22)`g
    B
    `2.12 xx 10^(21)`g
    C
    `2.12 xx 10^(23)` g
    D
    1280 g

  • A mole is a collection of 6.022 xx 10^23 particles and the number 6.022 xx 10^23 is called Avogadro number. The mass of this number of atoms in an element is equal to its gram atomic mass and mass of this number of molecules in a compound is equal to its gram molecular mass. The volume occupied by this number of molecules of a gas at N.T.P is 22.4 L. When 6.022 xx 10^23 molecules of a substance are dissolved in 1L of solution, the solution is known as 1 molar volume. Suppose the chemists would have choosen 10^20 as the number of particles in a mole, the mass of 1 mole of oxygen gas would be:

    A
    `5.32 xx 10^(3)` g
    B
    `5.32 xx 10^(-3)` g
    C
    `5.32 xx 10^(-23)` g
    D
    `5.32 xx 10^(3)` g

  • 6.022 xx 10^(22) molecules of N_(2) at NTP will occupy a volume of

    A
    22.4 litres
    B
    2.24 litres
    C
    6.02 litres
    D
    6.02 mL

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    Atoms and molecules are so small in size that it is neither possible to count them individually nor possible to determine their mass. These are counted collectively in terms of Avogadro's number. The mass of Avogadro's number of atoms and molecules is known as gram atomic mass and gram molecular mass respectively. The volume occupied by Avogadro's number of molecules of a gas or vapours is known as molar volume. The number of molecules in 16 g of methane is :

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