Question

Would you be able to fit a mole of rice in a 30.0m*8.5m*3.5m room??

Answer 1

Answer:

No.

Explanation:

1. Volume of a rice grain

There is no standard for the size of a rice grain, so let's make an arbitrary assumption.

An average rice grain behaves as if it were a rectangular solid with dimensions 7 mm × 2 mm × 2 mm.

The volume of one rice grain is

V = lwh = 7 mm × 2 mm × 2 mm = 28 mm³

Convert to cubic metres :

$V = \text{28 mm}^{3} \times \left (\dfrac{\text{1 m}}{\text{1000 mm}}\right )^{3} = \mathbf{2.8 \times 10^{-8}}\textbf{ m}^{\mathbf{3}}$

2. Volume of the room

V = lwh = 30.0 m × 8.5 m × 3.5 m = 890 m³

3. Volume of a mole of rice  

$V= 6.022 \times 10^{23}\text{ grains} \times \dfrac{2.8 \times 10^{-8}\text{ m}^{3}}{\text{1 grain }} = \mathbf{1.7 \times 10^{16}}\textbf{ m}^{\mathbf{3}}$

4. Conclusion

The room is not big enough to hold a mole of rice.

If you work it out, you will find that it takes about

20 000 000 000 000 (twenty trillion) rooms to hold a mole of rice.