QUESTION 8: HEAT. Calculate the increase in volume of the aluminium block, calculate the mass of the gas, calculate the mass of carbon dioxide that was added, calculate the volume of toluene that will overflow when the temperature increases to 48 °C.

The initial volume of the aluminium block is $V_0 = 0.420 \text{ m}^3$.
The initial temperature is $T_0 = 298 \text{ K}$.
The final temperature is $T_f = 358 \text{ K}$.
The change in temperature ($\Delta T$) is:

$$\Delta T = T_f - T_0 = 358 \text{ K} - 298 \text{ K} = 60 \text{ K}$$

The volumetric thermal expansion coefficient ($\beta$) for aluminium is not provided in the question. We will use a standard value for the linear thermal expansion coefficient of aluminium, $\alpha_{Al} = 23 \times 10^{-6} \text{ K}^{-1}$.
The volumetric thermal expansion coefficient is approximately three times the linear thermal expansion coefficient:

$$\beta_{Al} = 3 \alpha_{Al} = 3 \times (23 \times 10^{-6} \text{ K}^{-1}) = 69 \times 10^{-6} \text{ K}^{-1}$$

The formula for the increase in volume ($\Delta V$) due to thermal expansion is:

$$\Delta V = V_0 \beta_{Al} \Delta T$$

Substitute the values:

$$\Delta V = (0.420 \text{ m}^3) \times (69 \times 10^{-6} \text{ K}^{-1}) \times (60 \text{ K})$$ $$\Delta V = 1738.8 \times 10^{-6} \text{ m}^3$$ $$\Delta V = 0.0017388 \text{ m}^3$$

Rounding to three significant figures, the increase in volume is:

$$\Delta V = \boxed{\text{0.00174 m}^3}$$