Final answer:
To find the value of x in the formula Zn(NO3)2 . xH2O, we can use the provided information about the mass of anhydrous zinc nitrate compared to the mass of the hydrate. With the molar masses of zinc nitrate and water, we can set up an equation and solve for x.
Step-by-step explanation:
In order to find the value of x, we need to use the information provided. The mass of 1 mol of anhydrous zinc nitrate is 63.67% of the mass of 1 mol of the hydrate. This means that the anhydrous form of zinc nitrate is 63.67% of the hydrate form. We can set up the following equation:
63.67% = mass of anhydrous zinc nitrate / mass of hydrate
Simplifying this equation, we get:
0.6367 = mass of anhydrous zinc nitrate / (mass of anhydrous zinc nitrate + mass of water)
From the formula of the hydrate, we can see that the molar mass of zinc nitrate is 189.41 g/mol and the molar mass of water is 18.02 g/mol. With this information, we can calculate the mass of anhydrous zinc nitrate and the mass of water:
Let's assume 1 mol of the hydrate is Zn(NO3)2 · xH2O. The molar mass of Zn(NO3)2 is 189.41 g/mol and the molar mass of xH2O is 18.02x g/mol. Therefore, the mass of the hydrate is 189.41 + 18.02x g/mol.
Given that the mass of the anhydrous zinc nitrate is 63.67% of the mass of the hydrate, we can set up the equation:
63.67% = mass of anhydrous zinc nitrate / (mass of anhydrous zinc nitrate + mass of water)
0.6367 = (189.41 g/mol)/(189.41 g/mol + 18.02x g/mol)
Solving for x, we can find the value of x.