Mass of solute (NaCl)= 50gm mass of solvent (water)= 500gm mass of solution = mass of solute + mass of solvent =50gm+500gm =550gm concentration at 283 K = mass of solute ÷ mass of solvent =50÷550*100 =9.09%

Introduction:
In this problem, we are given the mass of sodium chloride (NaCl) and water, as well as the temperature at which they are mixed. We need to find the concentration of the resulting solution at this temperature.

Given data:
- Mass of sodium chloride (NaCl) = 50g
- Mass of water = 500g
- Temperature = 283K

Calculating moles of NaCl:
To find the concentration of the solution, we first need to calculate the number of moles of sodium chloride.

The molar mass of NaCl is 58.44 g/mol. We can use this to find the number of moles of NaCl:

Number of moles of NaCl = Mass of NaCl / Molar mass of NaCl
= 50g / 58.44 g/mol
= 0.856 moles

Calculating moles of water:
Next, we need to calculate the number of moles of water.

The molar mass of water (H2O) is 18.02 g/mol. We can use this to find the number of moles of water:

Number of moles of water = Mass of water / Molar mass of water
= 500g / 18.02 g/mol
= 27.75 moles

Calculating concentration:
The concentration of a solution is given by the formula:

Concentration (in mol/L) = Number of moles of solute / Volume of solution (in L)

In this case, the volume of the solution is the sum of the volumes of sodium chloride and water. However, since water is the solvent and its volume remains constant, we only need to consider the volume of sodium chloride.

To calculate the volume of sodium chloride, we need to convert the mass of NaCl to volume using its density. The density of NaCl is 2.165 g/cm³.

Volume of NaCl = Mass of NaCl / Density of NaCl
= 50g / 2.165 g/cm³
= 23.11 cm³

Now, we can calculate the concentration:

Concentration = Number of moles of NaCl / Volume of NaCl (in L)
= 0.856 moles / (23.11 cm³ / 1000 cm³/L)
= 37.04 mol/L

Conclusion:
The concentration of the sodium chloride solution at 283K is 37.04 mol/L.