Question

When 200. mL of 1.50 × 10^-4 M hydrochloric acid is added to 135 mL of 1.75 × 10^-4 M Mg(OH)₂, the resulting solution will be

Answer 1

Calculation:

1. Moles of H⁺ from HCl:

   $$n_{{\text{H}}^{+}}=0.200\text{L}\times 1.50\times 10^{-4}\text{M}=3.00\times 10^{-5}\text{moles}$$

$$=3.00\times 10^{-5}\text{moles}$$

1. Moles of OH⁻ from Mg(OH)₂:

   $$n$$$$n_{{\text{OH}}^{-}}=2\times 2.3625\times 10^{-5}=4.725\times 10^{-5}\text{moles}$$

2. $$=4.725\times 10^{-5}\text{moles}$$

3. Compare H⁺ and OH⁻:

   $${\text{Excess OH}}^{-}=4.725\times 10^{-5}-3.00\times 10^{-5}=1.725\times 10^{-5}\text{moles}$$

4. $$=1.725\times 10^{-5}\text{moles}$$

Result: The solution is basic (excess OH⁻)

Answer 2

Let's break down this problem step-by-step:

Understanding Perpetuity

A perpetuity is a stream of equal payments that continues forever. In this case, the preferred stock pays a fixed annual dividend of $4.80 indefinitely.

Present Value of a Perpetuity

The present value (PV) of a perpetuity is calculated using the following formula:

PV = Payment / Discount Rate

Where:

• PV is the present value of the perpetuity (the worth of the stock today).

• Payment is the fixed periodic payment (the annual dividend, $4.80).

• Discount Rate is the required rate of return (11% or 0.11).

Applying the Formula

Now, let's plug in the given values:

PV = $4.80 / 0.11

PV = $43.636363...

Rounding to Two Decimal Places

Since we're dealing with money, we round the result to two decimal places:

PV ≈ $43.64

Answer:

One share of this preferred stock is worth approximately $43.64 to you today if you require a rate of return of 11 percent.