Question

for every 1.0 mole of glycine in the sample, how many molecules of methionine are present? (for help performing calculations with numbers expressed in scientific
options:
○ $1.08 \times 10^{-70}$ molecules of methionine
● $1.8 \times 10^{-3}$ molecules of methionine
○ $1.08 \times 10^{21}$ molecules of methionine
○ $6.02 \times 10^{23}$ molecules of methionine
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this is the number of moles of methionine. you can find the number of methionine molecules per mole of glycine by multiplying the molar ratio by avogadros number: $(1.8 \times 1$ molecules/mole) = molecules of methionine per mole of glycine.
to multiply numbers expressed in scientific notation, add the exponents on 10 and multiply the other parts of the numbers separately.
$(\text{a} \times 10^n) \times (\text{b} \times 10^m) = (\text{a} \times \text{b}) \times 10^{n+m}$

Explanation:

Step1: Identify the molar ratio and Avogadro's number

Assume the molar ratio of methionine to glycine is \(1.8\times 10^{-3}\) moles of methionine per mole of glycine. Avogadro's number is \(6.02\times 10^{23}\) molecules/mole.

Step2: Multiply molar ratio by Avogadro's number

Using the formula for multiplying numbers in scientific notation \((a\times 10^{n})\times(b\times 10^{m})=(a\times b)\times 10^{n + m}\), where \(a = 1.8\), \(n=- 3\), \(b = 6.02\), \(m = 23\).
First, multiply the coefficients: \(1.8\times6.02 = 10.836\)
Then, add the exponents: \(-3+23 = 20\)
So, \(1.8\times 10^{-3}\times6.02\times 10^{23}=10.836\times 10^{20}\)
Convert to proper scientific notation: \(1.0836\times 10^{21}\approx1.08\times 10^{21}\)

Answer:

\(1.08\times 10^{21}\) molecules of methionine