If the masses of Cr and O are in the ratio 13 : 12 in CrO3, then the ratio of O that cobines with the same mass of Cr in Cr2O3 and Cr2O7 is

Options

A. `1 : 2`
B. `1 : 4`
C. `3 : 7`
D. `2 : 5`

Answer

To find the ratio of oxygen that combines with the same mass of chromium in Cr2O3 and Cr2O7, we can follow these steps:

### Step 1: Determine the molar masses of Cr and O
- The molar mass of chromium (Cr) is approximately 52 g/mol.
- The molar mass of oxygen (O) is approximately 16 g/mol.

### Step 2: Calculate the mass ratio in CrO3
- In CrO3, the ratio of Cr to O is given as 13:12.
- This means that for every 13 grams of Cr, there are 12 grams of O.
- Since CrO3 contains 1 Cr and 3 O, we can find the mass of oxygen that combines with 1 gram of Cr.

### Step 3: Find the mass of O that combines with 1 g of Cr in CrO3
- From the ratio, if 13 g of Cr combines with 12 g of O, then:
\[ \text{Mass of O per gram of Cr} = \frac{12 \text{ g O}}{13 \text{ g Cr}} = \frac{12}{13} \text{ g O} \]

### Step 4: Calculate the mass of O in Cr2O3
- In Cr2O3, there are 2 Cr and 3 O.
- The total mass of Cr in Cr2O3 is:
\[ 2 \times 52 \text{ g} = 104 \text{ g} \]
- The total mass of O in Cr2O3 is:
\[ 3 \times 16 \text{ g} = 48 \text{ g} \]
- The mass of O that combines with 104 g of Cr is 48 g.

### Step 5: Find the mass of O that combines with 1 g of Cr in Cr2O3
- The mass of O per gram of Cr in Cr2O3 is:
\[ \text{Mass of O per gram of Cr} = \frac{48 \text{ g O}}{104 \text{ g Cr}} = \frac{48}{104} = \frac{12}{26} = \frac{6}{13} \text{ g O} \]

### Step 6: Calculate the mass of O in Cr2O7
- In Cr2O7, there are 2 Cr and 7 O.
- The total mass of O in Cr2O7 is:
\[ 7 \times 16 \text{ g} = 112 \text{ g} \]
- The mass of O that combines with 104 g of Cr in Cr2O7 is 112 g.

### Step 7: Find the mass of O that combines with 1 g of Cr in Cr2O7
- The mass of O per gram of Cr in Cr2O7 is:
\[ \text{Mass of O per gram of Cr} = \frac{112 \text{ g O}}{104 \text{ g Cr}} = \frac{112}{104} = \frac{28}{26} = \frac{14}{13} \text{ g O} \]

### Step 8: Calculate the ratio of O in Cr2O3 to Cr2O7
- Now we have:
- Mass of O per gram of Cr in Cr2O3 = \( \frac{6}{13} \)
- Mass of O per gram of Cr in Cr2O7 = \( \frac{14}{13} \)
- The ratio of O in Cr2O3 to O in Cr2O7 is:
\[ \text{Ratio} = \frac{\frac{6}{13}}{\frac{14}{13}} = \frac{6}{14} = \frac{3}{7} \]

### Final Answer
The ratio of oxygen that combines with the same mass of chromium in Cr2O3 to Cr2O7 is **3:7**.

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