Question

A sample of municipal water contains one part of urea (m.wt=60) per million parts of water by weight. The number of urea molecules in a drop of water of volume 0.05ml is?​

Answer 1

Given:

• Municipal water contains one part of urea $(m.wt=60)$ per million parts of water by weight.

To Find:

• The number of urea molecules in a drop of water of volume $0.05ml$

Solution:

Taking into account that $1 ppm$ means $1 mg$ urea is in $1000 g$ of water

The mass of urea in 0.05 g

                  $m = \frac{1 mg \times 0.05 g }{1000g} = 5 \times 10^{-8}g.$

Then the number of moles for urea is defined by

             $\nu = \frac{m}{M_w}$

Here,

$m$ – mass of urea

$M_w$ – molecular weight of urea being of 60 g/mol.

Thus,

           $\nu = 5 \times 10^{-8} g /60 g mol^{-1} = 0.08333 \times 10^{-8} mole$

The number of urea molecules  

$N = \nu \times N_a$

Where

$N_a$ – the Avogadro constant $(6.02 \times 10^{23} mole^{-1})$

$N = 0.08333 \times 10^{-8} \ mole \times 6.02 \times 10^{23} \ mole^{-1}$

    $= 0.502 \times 10^{15} \ molecules$

Thus,

The number of urea molecules in a drop of water of volume $0.05ml$ is $0.502 \times 10^{15} \ molecules$

Answer 2

Answer:

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Explanation:

Taking into account that 1 ppm1ppm means 1 mg1mg urea is in 1000 g1000g of water

The mass of urea in 0.05 g

m = \frac{1 mg \times 0.05 g }{1000g} = 5 \times 10^{-8}g.m=

1000g

1mg×0.05g

=5×10

−8

g.

Then the number of moles for urea is defined by

\nu = \frac{m}{M_w}ν=

M

w

m

Here,

mm – mass of urea

M_wM

w

– molecular weight of urea being of 60 g/mol.

Thus,

\nu = 5 \times 10^{-8} g /60 g mol^{-1} = 0.08333 \times 10^{-8} moleν=5×10

−8

g/60gmol

−1

=0.08333×10

−8

mole

The number of urea molecules

N = \nu \times N_aN=ν×N

a

Where

N_aN

a

– the Avogadro constant (6.02 \times 10^{23} mole^{-1})(6.02×10

23

mole

−1

)

N = 0.08333 \times 10^{-8} \ mole \times 6.02 \times 10^{23} \ mole^{-1}N=0.08333×10

−8

mole×6.02×10

23

mole

−1

= 0.502 \times 10^{15} \ molecules=0.502×10

15

molecules

Thus,

The number of urea molecules in a drop of water of volume 0.05ml0.05ml is 0.502 \times 10^{15} \ molecules0.502×10

15

molecules