Sodium and oxygen combine to form two compounds, one of which is NaO. We are given that the percentage of sodium in the other compound is 59%. To find out the formula of this compound, we need to calculate the atomic ratio of sodium to oxygen.

Let's assume the formula of the other compound is NaX, where X represents the unknown element. To determine the formula, we can use the concept of percent composition.

Step 1: Calculate the percent composition of NaO
The formula for sodium oxide is NaO, which consists of one sodium atom (Na) and one oxygen atom (O). To calculate the percent composition of NaO, we need to find the molar mass of Na and O.

The atomic mass of sodium (Na) is 22.99 g/mol, and the atomic mass of oxygen (O) is 16.00 g/mol.

The molar mass of NaO = (1 x atomic mass of Na) + (1 x atomic mass of O) = (1 x 22.99 g/mol) + (1 x 16.00 g/mol) = 38.99 g/mol

Now, we can calculate the percent composition of Na in NaO:
% Na = (atomic mass of Na / molar mass of NaO) x 100
% Na = (22.99 g/mol / 38.99 g/mol) x 100 ≈ 59.11%

Step 2: Calculate the atomic ratio of sodium to oxygen in NaX
Now, let's consider the other compound NaX, where X represents the unknown element. We are given that the percentage of sodium in NaX is 59%.

Since the only elements in NaX are sodium (Na) and the unknown element (X), the total percentage of these two elements must add up to 100%.

% Na + % X = 100%
59% + % X = 100%
% X = 100% - 59% = 41%

Step 3: Determine the formula of NaX
Now that we know the percentage of X in NaX is 41%, we can write down the formula using the atomic ratio of sodium to X.

The atomic ratio of sodium to X in NaX can be written as:
1 : (41 / 59)

Simplifying this ratio, we get:
1 : (0.695)

To obtain whole numbers, we can multiply the ratio by a common factor. In this case, we can multiply by 1000 to eliminate the decimal points:

1000 : (0.695 x 1000) = 1000 : 695

Therefore, the formula for the other compound is Na695X1000.

Conclusion
The formula of the compound with 59% sodium is Na695X1000.