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muminat
3 years ago
11

A certain radioactive nuclide has a half life of 1.00 hour(s). Calculate the rate constant for this nuclide. s-1 Calculate the d

ecay rate for 1.000 mole of this nuclide. decays s-1
Chemistry
1 answer:
Karo-lina-s [1.5K]3 years ago
8 0

Answer:

k= 1.925×10^-4 s^-1

1.2 ×10^20 atoms/s

Explanation:

From the information provided;

t1/2=Half life= 1.00 hour or 3600 seconds

Then;

t1/2= 0.693/k

Where k= rate constant

k= 0.693/t1/2 = 0.693/3600

k= 1.925×10^-4 s^-1

Since 1 mole of the nuclide contains 6.02×10^23 atoms

Rate of decay= rate constant × number of atoms

Rate of decay = 1.925×10^-4 s^-1 ×6.02×10^23 atoms

Rate of decay= 1.2 ×10^20 atoms/s

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(b) 118 g Cr₂O₃

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Step 1: Convert 156 g Cr₂S₃ to moles

Cr Molar Mass - 52.00 g/mol × 2 = 104.00 g/mol

S Molar Mass - 32.07 g/mol × 3 = 96.21 g/mol

156 g Cr₂S₃ ÷ 200.21 g/mol = 0.779182 mol Cr₂S₃

Step 2: Find conversion from Cr₂S₃ to Cr₂O₃

1 mol Cr₂S₃ equals 1 mol Cr₂O₃

Step 3: Use Dimensional Analysis

0.779182 mol Cr₂S₃ · \frac{1 \hspace{2} mol \hspace{2} Cr_2O_3}{1 \hspace{2} mol \hspace{2} Cr_2S_3} = 0.779182 mol Cr₂O₃

0.779182 mol Cr₂O₃ ≈ 0.779 mol Cr₂O₃ (3 significant figures)

Step 4: Convert moles to grams

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O Molar Mass - 16.00 g/mol × 3 = 48.00 g/mol

0.779182 mol Cr₂O₃ · 152.00 g/mol = 118.436 g Cr₂O₃

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