Answer: The relative formula mass of Group 2 carbonate W is 36534 g/mol.
Explanation: We can use the ideal gas law to solve for the number of moles of gas produced:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Assuming standard temperature and pressure (STP), which is 273 K and 1 atm, we can write:
(1 atm) (24 dm³) = n (0.08206 L atm/mol K) (273 K)
Solving for n, we get:
n = 1.0 mol
So, one mole of the Group 2 carbonate W produces 24 dm³ of gas at STP.
To find the relative formula mass of W, we need to know the molar mass of the carbonate. Let's assume the formula of the carbonate is MCO₃, where M is the Group 2 metal.
From the ideal gas law, we know that:
PV = nRT
or
n = PV/RT
We can rearrange this equation to solve for the molar mass of the carbonate:
M = m/n = PV/RTm
where m is the mass of the carbonate and M is the molar mass.
Since we know the volume of gas produced and the conditions at which it was produced, we can calculate the number of moles of carbonate that decomposed to produce the gas:
n = PV/RT = (1 atm) (24 dm³) / (0.08206 L atm/mol K) (273 K) = 0.986 mol
The molar mass of the carbonate is then:
M = m/n = 36000 g / 0.986 mol = 36534 g/mol
So, the relative formula mass of Group 2 carbonate W is 36534 g/mol.