To solve the given problem, we need to analyze the chemical reaction between common salt (NaCl), potassium dichromate (\( K_2Cr_2O_7 \)), and concentrated sulfuric acid (\( H_2SO_4 \)). This reaction is known to produce a characteristic gas. Let's understand the reaction step by step:
- When a mixture of common salt (NaCl) and potassium dichromate (\( K_2Cr_2O_7 \)) is heated with concentrated sulfuric acid (\( H_2SO_4 \)), it produces chromium oxychloride as a gas, also known as chromyl chloride (\( CrO_2Cl_2 \)). The reaction is as follows:
\(4NaCl + K_2Cr_2O_7 + 6H_2SO_4 \rightarrow 2CrO_2Cl_2 + 2KHSO_4 + 4NaHSO_4 + 3H_2O\)
- In this reaction, the gas evolved is chromyl chloride (\( CrO_2Cl_2 \)).
- Let's determine the oxidation state of chromium in the evolved gas, chromyl chloride (\( CrO_2Cl_2 \)):
Chromyl chloride (\( CrO_2Cl_2 \)) has the following structure: \(CrO_2Cl_2: \ Cr + 2\times(-2) + 2\times(-1) = 0\)
Simplifying the equation for oxidation state:
\(Cr - 4 - 2 = 0 \\ Cr = +6\)
- Thus, the oxidation state of chromium in chromyl chloride (\( CrO_2Cl_2 \)) is +6.
- Hence, the correct option is that the formula of the gas evolved is \( CrO_2Cl_2 \), and the oxidation state of the central metal atom, chromium, is +6.
Therefore, the correct answer is the first option: \( CrO_2Cl_2 \) and +6.