Question

How many grams of SrO should be dissolved in sufficient water to make \(2.00 \mathrm{~L}\) of a solution with \(\mathrm{a} \mathrm{PH}=10.0\) ?

Short answer

0.01036 grams of SrO are required.

Step-by-step solution

Understanding pH and pOH

The given solution has a pH of 10.0. Use the relation between pH and pOH: \( \text{pH} + \text{pOH} = 14 \). Thus, \( \text{pOH} = 14 - 10 = 4 \).

Calculate Hydroxide Ion Concentration

We can find the hydroxide ion concentration \([\text{OH}^-]\) using \( \text{pOH} = -\log[\text{OH}^-] \). Therefore, \([\text{OH}^-] = 10^{-4} \text{ M} \).

Determine Moles of OH⁻ Needed

To find the total moles of \( \text{OH}^- \), use the formula: \( \text{moles} = \text{concentration} \times \text{volume} \). \( \text{Moles of } \text{OH}^- = 10^{-4} \text{ M} \times 2.00 \text{ L} = 2.00 \times 10^{-4} \text{ moles} \).

Understand SrO Dissociation

Strontium oxide (\( \text{SrO} \)) dissociates in water as \( \text{SrO} \rightarrow \text{Sr}^{2+} + \text{O}^{2-} \). In water, \( \text{O}^{2-} \) reacts with water to form \( 2 \text{OH}^- \) ions: \( \text{O}^{2-} + \text{H}_2\text{O} \rightarrow 2 \text{OH}^- \). So, 1 mole of \( \text{SrO} \) produces 2 moles of \( \text{OH}^- \).

Calculate Moles of SrO Required

Since 1 mole of \( \text{SrO} \) produces 2 moles of \( \text{OH}^- \), the moles of \( \text{SrO} \) required are \( \frac{2.00 \times 10^{-4}}{2} = 1.00 \times 10^{-4} \).

Calculate Mass of SrO Needed

Find the molar mass of \( \text{SrO} \): \( \text{Sr} = 87.62 \text{ g/mol} \), \( \text{O} = 16.00 \text{ g/mol} \). Thus, the molar mass of \( \text{SrO} \) is \( 87.62 + 16.00 = 103.62 \text{ g/mol} \). The mass of \( \text{SrO} \) required is \( 1.00 \times 10^{-4} \text{ moles} \times 103.62 \text{ g/mol} = 0.01036 \text{ g} \).

Key concepts

pH and pOH Relationship

In chemistry, the pH and pOH values are essential for understanding the acidity or basicity of a solution. The relationship between them is given by the equation:

• \( \text{pH} + \text{pOH} = 14 \)

This equation is helpful because it shows that knowing one of these values allows you to find the other. Let's consider a solution with a pH of 10.0.
Using the formula, we subtract the pH from 14 to get the pOH:

• \( \text{pOH} = 14 - 10 = 4 \)

A pH greater than 7 indicates a basic solution. The lower the value of pOH, the more basic the solution is. Understanding this relationship is crucial for solving many chemistry problems related to acids and bases.

Hydroxide Ion Concentration

The concentration of hydroxide ions \( [\text{OH}^-] \) in a solution is a key factor in determining its basicity. Once we know the pOH, \( [\text{OH}^-] \) can be easily calculated using the formula:

• \( \text{pOH} = -\log[\text{OH}^-] \)

To find \( [\text{OH}^-] \), we need to take the antilog:

• \([\text{OH}^-] = 10^{-\text{pOH}} = 10^{-4} \, \text{M} \)

This gives us the hydroxide ion concentration in molarity (M), which tells us there are \( 0.0001 \, \text{moles} \) of \( \text{OH}^- \) per liter of solution. Knowing the concentration of ions is very useful in chemical calculations, especially when working with solutions at equilibrium or when predicting reaction outcomes.

Stoichiometry

Stoichiometry involves using balanced chemical equations to determine the relationships between reactants and products. In this problem, strontium oxide (SrO) dissociates in water to eventually produce hydroxide ions. The balanced chemical equation for the dissociation is:

• \( \text{SrO} \rightarrow \text{Sr}^{2+} + \text{O}^{2-} \)
• \( \text{O}^{2-} + \text{H}_2\text{O} \rightarrow 2\text{OH}^- \)

These reactions show that one mole of SrO forms two moles of hydroxide ions. This stoichiometric relationship is crucial when determining how much SrO is needed to produce a specific amount of hydroxide ions. If we need \( 2.00 \text{ x } 10^{-4} \, \text{moles} \) of \( \text{OH}^- \), we only need half as many moles of SrO, which is \( 1.00 \text{ x } 10^{-4} \, \text{moles} \) because of the 1:2 ratio.

Molar Mass Calculations

Calculating the molar mass of a compound is a foundational part of determining how much material is needed in a chemical reaction. The molar mass is the mass of one mole of a substance, and it's calculated by adding up the atomic masses of its constituent elements.
For strontium oxide (SrO), the atomic mass of strontium (Sr) is \( 87.62 \, \text{g/mol} \), and for oxygen (O), it is \( 16.00 \, \text{g/mol} \). Thus, the molar mass of SrO is:

• \( 87.62 + 16.00 = 103.62 \, \text{g/mol} \)

Using the molar mass helps us find the mass of SrO needed to achieve the desired hydroxide concentration in the solution. We multiply the moles of SrO calculated (\( 1.00 \text{ x } 10^{-4} \, \text{moles} \) by the molar mass:

• \( 1.00 \times 10^{-4} \, \text{moles} \times 103.62 \, \text{g/mol} = 0.01036 \, \text{g} \)

This calculation tells us that to achieve the required hydroxide ion concentration, we need \( 0.01036 \, \text{g} \) of SrO.