Copper `(Cu)` and `(Zn)` react differently with `HNO_(3)` as follows:
`Cu + 4H^(o+) (aq) + 2NO_(3)^(ɵ) (aq) rarr 2NO_(2)(g) _ Cu^(2+) + 2H_(2)O`
`4Zn +10 H^(o+) (aq) + 2NO_(3)^(ɵ) (aq) rarr NH_(4)^(o+) + 4Zn^(2+) + 3H_(2)O`
What volume of `2.0 M HNO_(3)` would react with `10.0g` of a brass `(90.% Cu, 10.0% Zn)` according to the above equation?

Options

A. `~~ 100 mL`
B. `~~ 150 mL`
C. `~~ 200 mL`
D. `~~ 300 mL`

Explanation

To solve the problem, we need to determine the volume of 2.0 M HNO₃ that would react with 10.0 g of brass, which is composed of 90% copper and 10% zinc. We will follow these steps:

### Step 1: Calculate the mass of copper and zinc in the brass
Given that brass is 90% copper and 10% zinc, we can calculate the mass of each component in 10.0 g of brass.

- Mass of copper (Cu) = 90% of 10.0 g = 0.90 × 10.0 g = 9.0 g
- Mass of zinc (Zn) = 10% of 10.0 g = 0.10 × 10.0 g = 1.0 g

**Hint:** To find the mass of a component in a mixture, multiply the total mass by the percentage (as a decimal) of that component.

### Step 2: Calculate the moles of copper and zinc
Next, we need to convert the masses of copper and zinc into moles using their respective molar masses.

- Molar mass of copper (Cu) = 63.5 g/mol
- Molar mass of zinc (Zn) = 65.35 g/mol

Calculating the moles:

- Moles of copper = Mass of copper / Molar mass of copper = 9.0 g / 63.5 g/mol = 0.141 mol
- Moles of zinc = Mass of zinc / Molar mass of zinc = 1.0 g / 65.35 g/mol = 0.0153 mol

**Hint:** To calculate moles, use the formula: Moles = Mass (g) / Molar Mass (g/mol).

### Step 3: Determine the moles of HNO₃ required for each metal
Using the balanced chemical equations, we can find out how many moles of HNO₃ are required for the moles of copper and zinc.

1. For copper:
- From the reaction: 1 mol Cu reacts with 4 mol HNO₃
- Moles of HNO₃ required for copper = 0.141 mol Cu × 4 mol HNO₃/mol Cu = 0.564 mol HNO₃

2. For zinc:
- From the reaction: 4 mol Zn reacts with 10 mol HNO₃
- Moles of HNO₃ required for zinc = 0.0153 mol Zn × (10 mol HNO₃ / 4 mol Zn) = 0.03825 mol HNO₃

**Hint:** Use the stoichiometry from the balanced equations to convert moles of metal to moles of acid.

### Step 4: Calculate the total moles of HNO₃ required
Now, we will sum the moles of HNO₃ required for both copper and zinc.

Total moles of HNO₃ = Moles required for Cu + Moles required for Zn
Total moles of HNO₃ = 0.564 mol + 0.03825 mol = 0.60225 mol

**Hint:** To find the total amount needed, simply add the moles required for each component.

### Step 5: Calculate the volume of 2.0 M HNO₃ required
Using the molarity formula, we can find the volume of HNO₃ needed. Molarity (M) = Moles / Volume (L), so Volume (L) = Moles / Molarity.

Volume of HNO₃ = Total moles of HNO₃ / Molarity
Volume of HNO₃ = 0.60225 mol / 2.0 M = 0.301125 L

Converting to milliliters:
Volume in mL = 0.301125 L × 1000 mL/L = 301.125 mL

**Hint:** To convert liters to milliliters, multiply by 1000.

### Final Answer
The volume of 2.0 M HNO₃ that would react with 10.0 g of brass is approximately **301.1 mL**.