Question

If one synthesized every possible DNA molecule, each with 20 subunits, how much would your collection of molecules weigh? The average molecular mass of a DNA subunit is 165 g mol−1.

Answer 1

The weight of a collection of DNA molecules with 20 subunits can be calculated by multiplying the number of molecules by the average molecular mass of a DNA subunit. In this case, the collection would weigh approximately 1.72984 × 10^28 grams.

Step-by-step explanation:

To calculate the weight of a collection of DNA molecules, we need to determine the number of molecules and then multiply it by the average molecular mass of a DNA subunit. If each DNA molecule has 20 subunits, we can calculate the number of molecules by considering that each subunit is a separate molecule. The number of molecules would be 20 raised to the power of the number of subunits, which in this case is 20. So, the number of molecules would be 20^20. To calculate the weight of the collection, we would multiply the number of molecules by the average molecular mass of a DNA subunit, which is 165 g/mol.

Let's do the calculation:

1. Calculate the number of molecules: 20^20 = 1.048576 × 10^26 molecules
2. Calculate the weight of the collection: 1.048576 × 10^26 molecules * 165 g/mol = 1.72984 × 10^28 g

So, the collection of molecules would weigh approximately 1.72984 × 10^28 grams.

Answer 2

The total mass is 6.03 × 10⁻⁹ g

Step-by-step explanation:

There are 4 nucleobases that can take the place of each subunit: adenine, guanine, cytosine and thymine. If each DNA molecule has 20 subunits there are 4²⁰ possible combinations. The total mass is:

`4^(20) molecules * (20subunits)/(1molecule)  * (1mol of subunits)/(6.02 * 10^(23)subunits ) * (165g)/(1mol of subunits) =6.03 * 10^(-9) g`