(a) Determine the number of sodium ions in the chemical formula of albite, \(\mathrm{Na}_{x} \mathrm{AlSi}_{3} \mathrm{O}_{8} .(\mathbf{b})\) Determine the number of hydroxide ions in the chemical formula of tremolite, $\mathrm{Ca}_{2} \mathrm{Mg}_{5}\left(\mathrm{Si}_{4} \mathrm{O}_{11}\right)_{2}(\mathrm{OH})_{x}$.

In the first part of the exercise, we are given the chemical formula of albite: \(\mathrm{Na}_{x} \mathrm{AlSi}_{3} \mathrm{O}_{8}\). Here, the sodium ion is represented by Na and we are asked to find the value of x. In the second part of the exercise, we are given the chemical formula of tremolite: \(\mathrm{Ca}_{2} \mathrm{Mg}_{5}\left(\mathrm{Si}_{4}\mathrm{O}_{11}\right)_{2}(\mathrm{OH})_{x}\). Here, the hydroxide ion is represented by OH and we are asked to find the value of x.

In order to determine the values of x, we must first understand that chemical formulas must be electrically neutral. This means that the total positive charge from the ions must equal the total negative charge from the ions. For albite: Na has a +1 charge, Al has a +3 charge, Si has a +4 charge while O has a -2 charge. For tremolite: Ca has a +2 charge, Mg has a +2 charge, Si has a +4 charge, O has a -2 charge, and OH has a -1 charge.

In this step, we will calculate the positive and negative charges in the albite formula and find the number of sodium ions, keeping in mind that the formula must be electrically neutral. Positive charges: \(1x\) charge from \(\mathrm{Na}_{x}\) \(3\) charges from \(\mathrm{Al}\) Negative charges: \(12\) charges from \(\mathrm{Si}_{3}\) \(16\) charges from \(\mathrm{O}_{8}\) The total charge from positive ions must equal the total charge from negative ions: \(1x + 3 = 12 + 16\) Solving for x: \(x = 12 + 16 - 3 = 25\) Therefore, the number of sodium ions in the chemical formula of albite is 25.

In this step, we will calculate the positive and negative charges in the tremolite formula and find the number of hydroxide ions, keeping in mind that the formula must be electrically neutral. Positive charges: \(4\) charges from \(\mathrm{Ca}_{2}\) \(10\) charges from \(\mathrm{Mg}_{5}\) \(16\) charges from \(\mathrm{Si}_{4}\times 2\) (because of the subscript 2 outside the brackets) Negative charges: \(22\times 2\) charges from \(\mathrm{O}_{11}\times 2\) (because of the subscript 2 outside the brackets) \(1x\) charge from \(\mathrm{(OH)}_{x}\) The total charge from positive ions must equal the total charge from negative ions: \(4 + 10 + 16 = 22\times 2 + 1x\) Solving for x: \(x = 4 + 10 + 16 - 22\times 2 = 30 - 44 = -14\) However, we have a negative value for x, which is not possible for the number of ions in the formula. Going back to the negative charge calculation, there is an error: the hydroxide ion (OH) has a -1 charge, not the oxygen atom. So the number of negative charges should be calculated as follows: Negative charges: \(2\times 2\) charges from \(\mathrm{O}_{2}\times 2\) (from the hydroxide ion, with subscript 2 outside the brackets) Now, the total charge from positive ions must equal the total charge from negative ions: \(4 + 10 + 16 = 2\times 2 + 1x\) Solving for x: \(x = 4 + 10 + 16 - 2\times 2 = 30 - 4 = 26\) Therefore, the number of hydroxide ions in the chemical formula of tremolite is 26.