Question

Volume occupied by one molecule of water (density = $ \;1{{ }}g\;c{m^{ - 3}} $ )) is
(A) $ 3.0 \times {10^{ - 23}}c{m^{ - 3}} $
(B) $ 5.5 \times {10^{ - 23}}c{m^{ - 3}} $
(C) $ 9.0 \times {10^{ - 23}}c{m^{ - 3}} $
(D) $ 6.023 \times {10^{ - 23}}c{m^{ - 3}} $

Answer 1

Hint: At standard Temperature and Pressure, the molar volume is the volume involved by one mole of a substance component or a synthetic compound. It tends to be determined by isolating the molar mass by mass thickness. Molar gas volume is one mole of any gas at a particular temperature and weight has a fixed volume.

Complete step by step answer:
First, let us write down what is given to us. We were given;
Density of water as $ 1{g \mathord{\left/
 {\vphantom {g {c{m^3}}}} \right.
} {c{m^3}}} $ and
Molar mass of water is $ 18{g \mathord{\left/
 {\vphantom {g {mol}}} \right.
} {mol}} $
From this information let us calculate the molar volume and this is done as:
Molar volume = $ \dfrac{{18{g \mathord{\left/
 {\vphantom {g {mol}}} \right.
} {mol}}}}{{1{g \mathord{\left/
 {\vphantom {g {c{m^3}}}} \right.
} {c{m^3}}}}} $
And this equal to $ 18{{c{m^3}} \mathord{\left/
 {\vphantom {{c{m^3}} {mol}}} \right.
} {mol}} $
And from this let us now calculate volume
 $ \Rightarrow $ Volume of 1 molecule is given as
 $ \dfrac{{{V_m}}}{{{N_A}}} $ which is equal to: $ \dfrac{{{V_m}}}{{{N_A}}} = \dfrac{{18{{c{m^3}} \mathord{\left/
 {\vphantom {{c{m^3}} {mol}}} \right.
} {mol}}}}{{6.022 \times {{10}^{23}}/mol}} $
 $ \Rightarrow 2.989 \times {10^{ - 23}}c{m^3} $ $ \approx 3 \times {10^{ - 23}}c{m^3} $
Thus, the correct option is A.

Additional Information:
The Molar volume is straightforwardly relative to molar mass and contrarily corresponding to thickness. The recipe of the molar volume is communicated as
 $ {V_m} $ = Molar mass Density
Where $ {V_m} $ is the volume of the substance.
The standard temperature utilized is 273 Kelvin or $ {0^o}C $
Standard weight is 1 climate, i.e., $ 760{{ }}mm{{ }}Hg $ .
Tentatively, one mole of any gas possesses a volume of 22.4 liters at STP.

Note:
Somewhere in the range of 1971 and 2019, SI characterized the "measure of substance" as a different element of estimation, and the mole was characterized as the measure of substance that has the same number of constituent particles as there are molecules in 12 grams of carbon-12. In that period, the molar mass of carbon-12 was hence precisely $ 12{{ }}g/mol $ , by definition.