An acidic solution is mixed so that the mass ratio of nitric acid to water is 2:7, IF a total of 270 grams of acid solution is mixed, how many more grams of water are there than the nitric acid?

Options

A. 60
B. 110
C. 150
D. 210

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Define the Variables
Let:
- \( N \) = grams of nitric acid
- \( W \) = grams of water

### Step 2: Set Up the Ratios
We know from the problem that the mass ratio of nitric acid to water is \( 2:7 \). This can be expressed as:
\[ \frac{N}{W} = \frac{2}{7} \]
From this, we can express \( N \) in terms of \( W \):
\[ N = \frac{2}{7} W \]

### Step 3: Set Up the Total Mass Equation
We also know that the total mass of the acid solution is 270 grams, which gives us the equation:
\[ N + W = 270 \]

### Step 4: Substitute \( N \) in the Total Mass Equation
Now we can substitute the expression for \( N \) from Step 2 into the total mass equation:
\[ \frac{2}{7} W + W = 270 \]

### Step 5: Combine Like Terms
To combine the terms on the left, we can express \( W \) as \( \frac{7}{7} W \):
\[ \frac{2}{7} W + \frac{7}{7} W = \frac{9}{7} W \]
Thus, we have:
\[ \frac{9}{7} W = 270 \]

### Step 6: Solve for \( W \)
To isolate \( W \), multiply both sides by \( \frac{7}{9} \):
\[ W = 270 \times \frac{7}{9} \]
Calculating \( 270 \div 9 \) gives us \( 30 \), so:
\[ W = 30 \times 7 = 210 \text{ grams} \]

### Step 7: Calculate \( N \)
Now that we have \( W \), we can find \( N \):
\[ N = \frac{2}{7} W = \frac{2}{7} \times 210 \]
Calculating gives:
\[ N = 30 \times 2 = 60 \text{ grams} \]

### Step 8: Find the Difference
Finally, we need to find how many more grams of water there are than nitric acid:
\[ W - N = 210 - 60 = 150 \text{ grams} \]

### Conclusion
Thus, there are **150 grams more water than nitric acid**.