Question

1. the element sulfur has three known isotopes. complete the question as in problem one. a. sulfur 32: 95% 31,972 answer: ______ b. sulfur 33: 0.76% 32.911 c. sulfur 34: 4,24% 34..010

Explanation:

Step1: Recall the formula for average atomic mass

The average atomic mass of an element is calculated by taking the weighted average of the atomic masses of its isotopes, where the weights are the relative abundances (expressed as decimals) of each isotope. The formula is:
$$\text{Average Atomic Mass} = (m_1 \times f_1) + (m_2 \times f_2) + (m_3 \times f_3)$$
where \( m_i \) is the atomic mass of isotope \( i \) and \( f_i \) is the fractional abundance of isotope \( i \).

Step2: Convert percentages to fractions

• For Sulfur - 32: \( f_1 = \frac{95}{100} = 0.95 \), \( m_1 = 31.972 \)
• For Sulfur - 33: \( f_2 = \frac{0.76}{100} = 0.0076 \), \( m_2 = 32.911 \)
• For Sulfur - 34: \( f_3 = \frac{4.24}{100} = 0.0424 \), \( m_3 = 34.010 \) (assuming the typo "34..010" is "34.010")

Step3: Calculate the contribution of each isotope

• Contribution of Sulfur - 32: \( 31.972 \times 0.95 = 30.3734 \)
• Contribution of Sulfur - 33: \( 32.911 \times 0.0076 \approx 0.2491 \)
• Contribution of Sulfur - 34: \( 34.010 \times 0.0424 \approx 1.4420 \)

Step4: Sum the contributions

Add the three contributions together:
$$30.3734 + 0.2491 + 1.4420 = 32.0645$$

Answer:

The average atomic mass of sulfur is approximately \( 32.06 \) (or more precisely \( 32.0645 \))