Given a solution containing 2.00 × 10^{-3} M Ca^{2+} and 3.00 × 10^{-2} M SO_4^{2-}, what is the value of the charge (q) carried by the ions in 1.00 L of this solution? (Use the elementary charge e = 1.602 × 10^{-19} C.)

• A. q = 9.61 × 10^{1} C
• B. q = 1.28 × 10^{2} C
• C. q = 1.60 × 10^{1} C
• D. q = 3.20 × 10^{0} C

Answer: (C)

Verified step by step guidance

1. Identify the ions present in the solution and their concentrations: Ca^{2+} with concentration 2.00 \(\times\) 10^{-3} M and SO_4^{2-} with concentration 3.00 \(\times\) 10^{-2} M.
2. Calculate the number of moles of each ion in 1.00 L of solution by using the formula: moles = concentration (M) \(\times\) volume (L). Since the volume is 1.00 L, the moles equal the concentration values directly.
3. Determine the total number of ions for each species by multiplying the moles by Avogadro's number (N_A = 6.022 \(\times\) 10^{23} ions/mol): Number of ions = moles \(\times\) N_A.
4. Calculate the total charge contributed by each ion type using the formula: Charge (C) = number of ions \(\times\) charge per ion \(\times\) elementary charge (e), where the charge per ion is the magnitude of the ion's charge (2 for Ca^{2+} and SO_4^{2-}), and e = 1.602 \(\times\) 10^{-19} C.
5. Sum the charges from both ion types to find the total charge q carried by the ions in 1.00 L of solution.