What are the definitions and laws related to the mole, Boyle's Law, allotropes of carbon, molar mass calculations, and periods in the periodic table?

Molar mass of $\text{CO}_2 = 12 \text{ g/mol} + 2 \times (16 \text{ g/mol}) = 12 + 32 = 44 \text{ g/mol}$.

Number of moles = $\frac{\text{given mass}}{\text{molar mass}}$

The number of moles in $44 \text{ g}$ of $\text{CO}_2$ is $\boxed{1.0 \text{ mol}}$.

5. What is meant by a period in the periodic table? (2 marks)
A period in the periodic table is a horizontal row of elements. Elements within the same period have the same number of electron shells.

6. State Avogadro's constant (1 mark)
Avogadro's constant is approximately $\boxed{6.022 \times 10^{23} \text{ mol}^{-1}}$.

7. What type of bonding exists in sodium chloride? (1 mark)
The type of bonding that exists in sodium chloride is ionic bonding.

8. State one use of graphite (1 mark)
One use of graphite is as a lubricant due to its layered structure allowing layers to slide past each other easily.

9. Convert $25^\circ\text{C}$ to Kelvin (2 marks)
To convert temperature from Celsius to Kelvin, use the formula: $\text{K} = ^\circ\text{C} + 273.15$.

$25^\circ\text{C}$ is equal to $\boxed{298.15 \text{ K}}$.

10. Distinguish between ionic and covalent bonding (2 marks)
Ionic bonding involves the transfer of electrons between atoms, typically a metal and a non-metal, forming oppositely charged ions that are held together by electrostatic forces. Covalent bonding involves the sharing of electrons between atoms, typically two non-metals, to achieve stable electron configurations.

11. State one reason why noble gases are unreactive (2 marks)
Noble gases are unreactive because they have a full outermost electron shell (a stable octet, or duplet for helium). This stable electron configuration means they do not readily gain, lose, or share electrons with other atoms.

12. Calculate the molar mass of $\text{CaCO}_3$ ($\text{Ca}=40, \text{C}=12, \text{O}=16$) (2 marks)
Molar mass of $\text{CaCO}_3 = (\text{atomic mass of Ca}) + (\text{atomic mass of C}) + 3 \times (\text{atomic mass of O})$

The molar mass of $\text{CaCO}_3$ is $\boxed{100 \text{ g/mol}}$.

13. What is meant by atomic radius? (2 marks)
The atomic radius is a measure of the size of an atom, typically defined as half the distance between the nuclei of two identical atoms that are bonded together.

14. State one property of ionic compounds (1 mark)
One property of ionic compounds is that they generally have high melting and boiling points.

15. What is meant by molar mass? (2 marks)
Molar mass is the mass of one mole of a substance. It is expressed in grams per mole ($\text{g/mol}$) and is numerically equal to the atomic mass (for elements) or molecular/formula mass (for compounds) in atomic mass units (amu).

16. State the number of groups in the periodic table (1 mark)
There are $\boxed{18}$ groups in the periodic table.

17. State Charles Law (2 marks)
Charles's Law states that for a fixed amount of gas at constant pressure, the volume of the gas is directly proportional to its absolute temperature.
Mathematically, this can be expressed as $\frac{V_1}{T_1} = \frac{V_2}{T_2}$.