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  • Calculating the Composition of a NaCl-NaBr Mixture
    Here's how to solve this problem:

    1. Find the mass of Cl and Br:

    * Since the mixture only contains Na, Cl, and Br, the mass of Cl and Br combined is:

    2.03 g (total mass) - 0.76 g (mass of Na) = 1.27 g

    2. Set up a system of equations:

    * Let 'x' represent the mass of NaCl and 'y' represent the mass of NaBr.

    * We know the following:

    * x + y = 1.27 g (total mass of Cl and Br)

    * The mass of Na in NaCl is proportional to the mass of NaCl (x)

    * The mass of Na in NaBr is proportional to the mass of NaBr (y)

    3. Calculate the proportion of Na in each compound:

    * NaCl:

    * Molar mass of NaCl = 58.44 g/mol

    * Molar mass of Na = 22.99 g/mol

    * Proportion of Na in NaCl = 22.99 g/mol / 58.44 g/mol = 0.393

    * NaBr:

    * Molar mass of NaBr = 102.89 g/mol

    * Molar mass of Na = 22.99 g/mol

    * Proportion of Na in NaBr = 22.99 g/mol / 102.89 g/mol = 0.223

    4. Set up the equation for the total mass of Na:

    * 0.393x + 0.223y = 0.76 g (This represents the total mass of Na in the mixture)

    5. Solve the system of equations:

    * You now have two equations with two unknowns:

    * x + y = 1.27

    * 0.393x + 0.223y = 0.76

    * You can solve this system using substitution or elimination. Here's the solution using elimination:

    * Multiply the first equation by -0.223: -0.223x - 0.223y = -0.283

    * Add this equation to the second equation: 0.17x = 0.477

    * Solve for x: x = 0.477 / 0.17 = 2.81 g (This is the mass of NaCl)

    * Substitute the value of x back into the first equation: 2.81 + y = 1.27

    * Solve for y: y = 1.27 - 2.81 = -1.54 g

    6. Interpret the result:

    * The result for y is negative, which means our assumption that the mass of NaBr was positive is incorrect. This indicates that the mixture is likely composed of only NaCl and does not contain NaBr.

    Therefore, the mixture consists of 2.81 grams of NaCl and no NaBr. It's important to note that this result doesn't make sense in the context of the problem. It's possible that there is an error in the given data.

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