Question

A mole is the number of particles of a substance with a mass equivalent to its molecular (or atomic) mass in daltons. There are $6.022\times {10}^{23}$molecules (or atoms) in 1.0 mole (Avogadro’s number; see Concept 3.2). The data table shows the “molar ratios" of some of the products from the Miller H₂S experiment. In a molar ratio, each unit’s value is expressed relative to a standard for that experiment. Here, the standard is the number of moles of the amino acid glycine, which is set to a value of 1.0. For instance, serine has a molar ratio of $3.0\times {10}^{-2}$, meaning that for every mole of glycine, there is $3.0\times {10}^{-2}$mole of serine.

(a) Give the molar ratio of methionine to glycine and explain what it means.

(b) How many molecules of glycine are present in 1.0 mole?

(c) For every 1.0 mole of glycine in the sample, how many molecules of methionine are present? (Recall that to multiply two numbers with exponents, you add their exponents; to divide them, you subtract the exponent in the denominator from that in the numerator.)

Short answer

(a) The molar ratio of the methionine to glycine is $1.8\times {10}^{-3}$.

(b) $6.02\times {10}^{23}$molecules of glycine are present in 1 mole of glycine.

(c) $6.02\times {10}^{22}$molecules of methionine are present for every 1 mole of glycine.

Step-by-step solution

Gram atom concept

One gram atom of an element is known to be the collection of $6.022\times {10}^{23}$particles. It is applicable in the case of atoms that have polyatomic states like oxygen, chlorine, sulfur, and many more.

One can calculate the atomic mass by dividing the group of 1 atom of an element by one-twelfth weight of carbon-12. It is an important concept that gives the idea about the nuclei of radioactive elements.

 Explanation for part (a)

The molar ratio is the proportion of the reactant and products for the particular reaction. The percentage of the methionine to glycine can be determined by calculating the balance of the methionine to glycine. It will be $1.8\times {10}^{-3}$.

Explanation for part (b)

The gram mole is the term used to define the collection of the $6.02\times {10}^{23}$molecules of an element or ions that form 1 mole of a substance.

So, one can simply say that $6.02\times {10}^{23}$molecules of glycine are present in 1 mole of glycine. This number is known as the Avogadro’s number.

Explanation for part (c)

Methionine amount per mole of glycine can be calculated by multiplying the molar ratio with $6.02\times {10}^{23}$. It will come out as $6.02\times {10}^{22}$.