Explain graphite's uses, convert 25C to Kelvin, why noble gases are unreactive, calculate CaCO3 molar mass, and define atomic radius.

Here are the answers to your questions:

8. One use of graphite is as a lubricant (due to its layered structure allowing layers to slide past each other easily). It is also used in pencils and as electrodes.

9. To convert $25^\circ\text{C}$ to Kelvin:

   $$\text{Temperature in Kelvin} = \text{Temperature in Celsius} + 273.15$$ $$\text{Temperature in Kelvin} = 25 + 273.15$$ $$\text{Temperature in Kelvin} = 298.15 \text{ K}$$

   The temperature is $\boxed{\text{298.15 K}}$.

10. Noble gases are unreactive because they have a full outer electron shell (a stable octet, or duet for helium). This electron configuration makes them very stable and they have no tendency to gain, lose, or share electrons.

11. To calculate the molar mass of $\text{CaCO}_3$: Given atomic masses: $\text{Ca}=40$, $\text{C}=12$, $\text{O}=16$.

    $$\text{Molar mass of } \text{CaCO}_3 = (1 \times \text{Ca}) + (1 \times \text{C}) + (3 \times \text{O})$$ $$\text{Molar mass of } \text{CaCO}_3 = (1 \times 40) + (1 \times 12) + (3 \times 16)$$ $$\text{Molar mass of } \text{CaCO}_3 = 40 + 12 + 48$$ $$\text{Molar mass of } \text{CaCO}_3 = 100 \text{ g/mol}$$

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

12. Atomic radius is defined as the distance from the center of the nucleus to the outermost electron shell of an atom.

13. One property of an ionic compound is that it typically has a high melting point. (Other properties include high boiling points, being soluble in polar solvents like water, and conducting electricity when molten or dissolved in water).

14. Molar mass is defined as the mass of one mole of a substance. It is expressed in grams per mole ($\text{g/mol}$).

15. The periodic table has $\boxed{\text{18 groups}}$.

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

17. To calculate the volume of the gas at $250 \text{ kPa}$, we use Boyle's Law, which states that for a fixed mass of gas at constant temperature, the pressure is inversely proportional to its volume ($P_1V_1 = P_2V_2$).