Answer :
To determine which of the given K values represents the strongest base, we need to understand that the strength of a base is related to its \(K_b\) (base dissociation constant) value. A higher \(K_b\) value indicates that the base is stronger because it means that the base ionizes more in solution, essentially meaning it produces more hydroxide ions (\(OH^-\)).
Let's compare the given K values:
A. \( K = 1.8 \times 10^{-5} \)
B. \( K = 1.26 \times 10^{-6} \)
C. \( K = 1.26 \times 10^{-7} \)
D. \( K = 3.8 \times 10^{-10} \)
Comparing the exponents first, since the negative exponents signify how small the number is, a less negative exponent corresponds to a bigger value. Therefore:
- The exponent -5 in option A is less negative than the exponents -6, -7, and -10 in options B, C, and D respectively.
- Therefore, \( 10^{-5} > 10^{-6} > 10^{-7} > 10^{-10} \).
Next, we should compare the coefficients (the numbers before the \( \times 10^{-\text{exponent}} \)):
- For exponents that are not equal, there is no need to compare coefficients, as the magnitude of the difference in the exponents will have a far more significant effect on the overall value. This tells us that option A must be larger than the others since its exponent is the highest.
Thus, we can conclude that option A \( K = 1.8 \times 10^{-5} \) is the largest K value and hence represents the strongest base of the choices given.
