Q. What is the mass in grams of \(5.90\ \text{mol}\ \mathrm{C_8H_{18}}\)?

We want the mass (in grams) of a given amount of a substance. The usual relationship is

\[ \text{mass} = \text{moles}\times \text{molar mass} \]

We are given \(5.90\ \text{mol}\) of \( \text{C}_8\text{H}_{18}\). So we need the molar mass of \( \text{C}_8\text{H}_{18}\).

Step 1: Find the molar mass of \( \text{C}_8\text{H}_{18}\)

Use atomic masses (in grams per mole):

\[ \text{C} \approx 12.01\ \text{g/mol}, \quad \text{H} \approx 1.008\ \text{g/mol} \]

The molar mass of \( \text{C}_8\text{H}_{18}\) is computed by multiplying each atomic mass by the number of atoms, then adding:

\[ \text{molar mass} = 8(12.01) + 18(1.008) \]

Compute each part:

\[ 8(12.01) = 96.08 \]

\[ 18(1.008) = 18.144 \]

Add them:

\[ \text{molar mass} = 96.08 + 18.144 = 114.224\ \text{g/mol} \]

With proper rounding for typical chemistry calculations, we can use \(114.22\ \text{g/mol}\) (or keep \(114.224\) until the final step).

Step 2: Convert moles to mass

Now use

\[ \text{mass} = 5.90\ \text{mol} \times 114.224\ \text{g/mol} \]

Multiply:

\[ \text{mass} = 5.90 \times 114.224 = 673.9216\ \text{g} \]

Step 3: Apply significant figures

The given number \(5.90\) has 3 significant figures. The molar mass from atomic masses is based on standard rounded values, and the final result should be reported to 3 significant figures.

So we round \(673.9216\) to 3 significant figures:

\[ \text{mass} \approx 674\ \text{g} \]

Final Answer: \(\boxed{674\ \text{g}}\)