State Hess's Law of constant heat summation. ii. From the H enthalpy values, determine the amount of energy liberated when 1 mol of ethanol is completely burnt under standard conditions. iii. Balance the following chemical equations.

1. $C(s) + O_2(g) \rightarrow CO_2(g)$ $\Delta H_c^\circ = -393.5 \text{ kJmol}^{-1}$
2. $H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l)$ $\Delta H_c^\circ = -285.8 \text{ kJmol}^{-1}$
3. $2C(s) + 3H_2(g) + \frac{1}{2}O_2(g) \rightarrow C_2H_5OH(l)$ $\Delta H_f^\circ = -227.6 \text{ kJmol}^{-1}$

• Reverse equation (3): $C_2H_5OH(l) \rightarrow 2C(s) + 3H_2(g) + \frac{1}{2}O_2(g)$ $\Delta H = -(-227.6 \text{ kJmol}^{-1}) = +227.6 \text{ kJmol}^{-1}$
• Multiply equation (1) by 2: $2C(s) + 2O_2(g) \rightarrow 2CO_2(g)$ $\Delta H = 2 \times (-393.5 \text{ kJmol}^{-1}) = -787.0 \text{ kJmol}^{-1}$
• Multiply equation (2) by 3: $3H_2(g) + \frac{3}{2}O_2(g) \rightarrow 3H_2O(l)$ $\Delta H = 3 \times (-285.8 \text{ kJmol}^{-1}) = -857.4 \text{ kJmol}^{-1}$

Adding the modified equations gives:
$C_2H_5OH(l) + 2C(s) + 3H_2(g) + 2O_2(g) + \frac{3}{2}O_2(g) \rightarrow 2C(s) + 3H_2(g) + \frac{1}{2}O_2(g) + 2CO_2(g) + 3H_2O(l)$
After canceling common species, we get the target reaction:
$C_2H_5OH(l) + 3O_2(g) \rightarrow 2CO_2(g) + 3H_2O(l)$

$\Delta H_{combustion}^\circ = (+227.6 \text{ kJmol}^{-1}) + (-787.0 \text{ kJmol}^{-1}) + (-857.4 \text{ kJmol}^{-1})$
$\Delta H_{combustion}^\circ = 227.6 - 787.0 - 857.4 \text{ kJmol}^{-1}$
$\Delta H_{combustion}^\circ = -1416.8 \text{ kJmol}^{-1}$
The amount of energy liberated is the absolute value of the enthalpy change.
The energy liberated is $\boxed{\text{1416.8 kJ}}$.

2.a. Balance the ff chemical equations.

• i) $Na_2SO_3 + HCl \rightarrow NaCl + SO_2 + H_2O$ $$Na_2SO_3 + 2HCl \rightarrow 2NaCl + SO_2 + H_2O$$
• ii) $Au + CN^- + H_2O \rightarrow [Au(CN)_2]^- + OH^-$ This reaction is typically balanced with oxygen ($O_2$) as an additional reactant. Assuming the presence of $O_2$ from the environment, the balanced equation is: $$4Au(s) + 8CN^-(aq) + O_2(g) + 2H_2O(l) \rightarrow 4[Au(CN)_2]^-(aq) + 4OH^-(aq)$$

2.b) List two essential parts of the mass spectrometer.

• Ionization chamber
• Detector

2.c) Why are gamma rays more injurious to health than alpha particles?
Gamma rays are more injurious to health than alpha particles primarily due to their high penetrating power. Gamma rays are high-energy electromagnetic radiation that can pass through significant amounts of matter, including the human body, causing damage to internal organs and DNA throughout the body. Alpha particles, while having high ionizing power, have very low penetrating power and are easily stopped by the skin, limiting their damage to superficial tissues unless ingested or inhaled.

2.d) The atomic mass of Carbon 12 is $1.6603 \times 10^{-24} \text{ g}$. If the mass of an atom is $5.313 \times 10^{-23} \text{ g}$, determine the relative atomic mass.

The mass of one Carbon-12 atom is $1.6603 \times 10^{-24} \text{ g}$. This value is equivalent to 1 atomic mass unit (amu).
Mass of the unknown atom = $5.313 \times 10^{-23} \text{ g}$.

Relative atomic mass is defined as the ratio of the mass of an atom to $\frac{1}{12}$ the mass of a carbon-12 atom (which is 1 amu).

Rounding to four significant figures:
The relative atomic mass is $\boxed{\text{32.00}}$.

2.e.i) Give 2 physical properties of metals.

• Good conductors of electricity
• Malleable

2.e.ii) Indicate how each of the properties given in (i) contribute to their characteristics/uses.

• Good conductors of electricity: Metals have delocalized electrons that are free to move throughout the metallic lattice, allowing them to efficiently carry electrical current. This property makes them ideal for electrical wiring and electronic components.
• Malleable: Metals can be hammered or pressed into thin sheets without breaking because the metallic bonds allow layers of atoms to slide past each other without fracturing the overall structure. This makes metals suitable for shaping into various forms, such as car bodies or aluminum foil.