Which of the following solutions have the same concentration?(a) 20 g of NaOH in 200 mL of solution (b) 0.5 mol of KC1 in 200 mL of solution (c) 40 g of NaOH in 100 mL of solution (d) 20 g of KOH in 200 mL of solution"

To determine which solutions have the same concentration, we need to calculate the molarity of each solution.

Molarity (MM) is defined as the number of moles of solute per liter of solution. However, the given amounts are not in moles or liters, so we first need to convert them to moles and liters, respectively.

Given: (a) 20 g20g of NaOHNaOH in 200 mL200mL of solution (b) 0.5 mol0.5mol of KClKCl in 200 mL200mL of solution (c) 40 g40g of NaOHNaOH in 100 mL100mL of solution (d) 20 g20g of KOHKOH in 200 mL200mL of solution

Let's calculate the molarity of each solution:

(a) For NaOHNaOH:

• Molar mass of NaOHNaOH = 22.99 g/mol22.99g/mol (for Na) + 16.00 g/mol16.00g/mol (for O) + 1.01 g/mol1.01g/mol (for H) = 39.99 g/mol39.99g/mol
• Number of moles of NaOHNaOH = 20 g39.99 g/mol=0.50 mol39.99g/mol20g=0.50mol
• Volume of solution = 200 mL=0.200 L200mL=0.200L
• Molarity (MM) = 0.50 mol0.200 L=2.5 M0.200L0.50mol=2.5M

(b) For KClKCl:

• Since the solution is already given in moles, we don't need to perform any additional calculations.
• Molarity (MM) = 0.5 M0.5M

(c) For NaOHNaOH:

• Number of moles of NaOHNaOH = 40 g39.99 g/mol=1.00 mol39.99g/mol40g=1.00mol
• Volume of solution = 100 mL=0.100 L100mL=0.100L
• Molarity (MM) = 1.00 mol0.100 L=10.0 M0.100L1.00mol=10.0M

(d) For KOHKOH:

• Molar mass of KOHKOH = 39.10 g/mol39.10g/mol (for K) + 16.00 g/mol16.00g/mol (for O) + 1.01 g/mol1.01g/mol (for H) = 56.11 g/mol56.11g/mol
• Number of moles of KOHKOH = 20 g56.11 g/mol≈0.356 mol56.11g/mol20g≈0.356mol
• Volume of solution = 200 mL=0.200 L200mL=0.200L
• Molarity (MM) = 0.356 mol0.200 L≈1.78 M0.200L0.356mol≈1.78M

Comparing the molarities, we can see that option (a) and option (d) have the same molarity of 2.5 M2.5M.

So, the correct answer is:

(a) 20 g of NaOH in 200 mL of solution and (d) 20 g of KOH in 200 mL of solution