Study sheet: Solutions and Ideal Gases

📋 Course Outline

1. Solution Preparation by Dissolution
2. Ionic Solid Dissolution
3. Solution Preparation by Dilution
4. Mass Percentage and Density
5. Ideal Gas Model and Law
6. Molar Volume and Gas Quantity
7. Calcium Carbonate Analysis

📖 1. Solution Preparation by Dissolution

★ Must-know

📐 Formula — The mass of solute to dissolve is given by $m_{\text{solute}}=n_{\text{solute}}M_{\text{solute}}=C_{\text{solute}}V_{\text{solution}}M_{\text{solute}}$.

Further detail

• Preparing a solution by dissolution consists of determining the required mass of solid solute and dissolving it in the chosen solvent volume.

💡 Memory Hook

solid solute → amount of substance → mass to dissolve

📖 2. Ionic Solid Dissolution

🔑 Key Concepts & Definitions

• Ionic solid dissolution : separates the solid into aqueous ions

★ Must-know

• Dissolution of iron(III) chloride is represented by $\mathrm{FeCl_3(s)}\xrightarrow{\text{water}}\mathrm{Fe^{3+}(aq)}+3\mathrm{Cl^-(aq)}$.

📐 Formula — For an FeCl₃ solution, the chloride ion concentration satisfies $[\mathrm{Cl^-}]=3C(\mathrm{FeCl_3})$.

Further detail

📐 Formula — For an FeCl₃ solution, the iron(III) ion concentration satisfies $[\mathrm{Fe^{3+}}]=C(\mathrm{FeCl_3})$.

💡 Memory Hook

dissolution of FeCl₃ → Fe³⁺ and 3 Cl⁻ in water

📖 3. Solution Preparation by Dilution

📝 Essential Points

📐 Formula — During dilution, conservation of amount of solute gives $C_{\text{daughter}}V_{\text{daughter}}=C_{\text{mother}}V_{\text{mother}}$.

📐 Formula — The dilution factor is $F=\frac{V_{\text{daughter}}}{V_{\text{mother}}}=\frac{C_{\text{mother}}}{C_{\text{daughter}}}$.

💡 Memory Hook

mother solution is concentrated, daughter solution is diluted

📖 4. Mass Percentage and Density

🔑 Key Concepts & Definitions

• Mass percentage : the mass of solute dissolved in 100 g of solution; for example, a 0.9% saline solution contains 0.9 g of salt in 100 g of serum

★ Must-know

📐 Formula — The mass fraction is $p_m=w=\frac{m_{\text{solute}}}{m_{\text{solution}}}$ and is dimensionless, while the mass percentage is $p_{m'}=w' =\frac{m_{\text{solute}}}{m_{\text{solution}}}\times100$ and is expressed as a percentage.

Further detail

📐 Formula — The mass fraction can be related to mass concentration and solution density by $w=\frac{C_{m(\text{solute})}}{\rho_{\text{solution}}}=\frac{C_{m(\text{solute})}}{d(\text{solution})\rho_{\text{water}}}$.

• The density of water is given as $\rho_{\text{water}}=1.00\,\mathrm{kg\,L^{-1}}=1.00\,\mathrm{g\,mL^{-1}}=1000\,\mathrm{kg\,m^{-3}}$.

📖 5. Ideal Gas Model and Law

🔑 Key Concepts & Definitions

• Ideal gas : a gas whose entities are sufficiently far apart to have no interactions and whose total proper volume is much smaller than the total gas volume

★ Must-know

📐 Formula — The ideal-gas law relates pressure, volume, amount of substance, and temperature through $PV=nRT$, where $R=8.314\,\mathrm{Pa\,m^3\,mol^{-1}\,K^{-1}}$ in SI units.

Further detail

📐 Formula — Temperature conversion is given by $T(\mathrm K)=\theta(^{\circ}\mathrm C)+273.15$.

📌 The ideal-gas model is valid only at low pressures and at temperatures far from the gas boiling temperature.

• For 5.0 L of hydrogen at 20 °C and the stated pressure, the amount of hydrogen is calculated as 0.21 mol using $n=\frac{PV}{RT}$.

💡 Memory Hook

higher temperature at fixed pressure → larger gas volume

📖 6. Molar Volume and Gas Quantity

🔑 Key Concepts & Definitions

• Molar volume : the volume occupied by one mole of gas and satisfies $V_m=\frac{RT}{P}$

★ Must-know

📐 Formula — At a given temperature and pressure, the amount of gas is related to its volume by $n=\frac{V}{V_m}$.

• The molar volume is 22.4 L mol⁻¹ at 0 °C and 1013 hPa, and 24.1 L mol⁻¹ at 20 °C and 1013 hPa.

Further detail

📌 At constant pressure, increasing the temperature increases the volume occupied by a gas.

💡 Memory Hook

gas volume → molar volume → amount of substance

📖 7. Calcium Carbonate Analysis

📝 Essential Points

📐 Formula — For 72 mL of carbon dioxide at 20 °C and 1013 hPa, the amount of carbon dioxide is $n_{\mathrm{CO_2}}=\frac{72\times10^{-3}}{24.1}=3.0\times10^{-3}\,\mathrm{mol}$.

📐 Formula — Using the reaction stoichiometry, the calcium carbonate amount equals the carbon dioxide amount, so its mass is $m_{\mathrm{CaCO_3}}=nM=3.0\times10^{-3}\times(40.1+12+3\times15)=0.30\,\mathrm g$.

• For the stated sample, the calcium carbonate mass percentage in the soil is 25%.

• Determining the calcium carbonate content of soil uses excess hydrochloric acid, measures the carbon dioxide volume, converts it to an amount of substance, obtains the calcium carbonate mass, and calculates the soil mass percentage.

💡 Memory Hook

CO₂ volume → CO₂ amount → CaCO₃ mass → mass percentage

📊 Synthesis Tables

Solution Preparation Methods

Method	Starting material	Key relation
Dissolution	Solid solute	$m=nM=CV M$
Dilution	Mother solution	$C_dV_d=C_mV_m$