If you mix 20.0 mL of a 3.00 M sugar solution with 30.0 mL of a 5.57 M sugar solution, you will end up with a sugar solution of_______.
To find the concentration of the resulting sugar solution after mixing, we can use the equation:
\(M_1 \cdot V_1 + M_2 \cdot V_2 = M_{\text{final}} \cdot V_{\text{final}}\)
Where:
\(M_1\) is the concentration of the first sugar solution,
\(V_1\) is the volume of the first sugar solution,
\(M_2\) is the concentration of the second sugar solution,
\(V_2\) is the volume of the second sugar solution,
\(M_{\text{final}}\) is the concentration of the resulting sugar solution, and
\(V_{\text{final}}\) is the total volume of the resulting sugar solution.
Given:
\(M_1 = 3.00 \, \text{M}\),
\(V_1 = 20.0 \, \text{mL}\),
\(M_2 = 5.57 \, \text{M}\),
\(V_2 = 30.0 \, \text{mL}\).
Substituting these values into the equation:
\(3.00 \, \text{M} \cdot 20.0 \, \text{mL} + 5.57 \, \text{M} \cdot 30.0 \, \text{mL} = M_{\text{final}} \cdot V_{\text{final}}\)
\(60.0 \, \text{moles/L} \cdot \text{mL} + 167.1 \, \text{moles/L} \cdot \text{mL} = M_{\text{final}} \cdot (20.0 \, \text{mL} + 30.0 \, \text{mL})\)
\(227.1 \, \text{moles/L} \cdot \text{mL} = M_{\text{final}} \cdot 50.0 \, \text{mL}\)
To find the concentration of the resulting sugar solution, divide both sides of the equation by \(50.0 \, \text{mL}\):
\(M_{\text{final}} = \frac{227.1 \, \text{moles/L} \cdot \text{mL}}{50.0 \, \text{mL}}\)
Simplifying the equation gives us:
\(M_{\text{final}} = 4.542 \, \text{M}\)
Therefore, mixing 20.0 mL of a 3.00 M sugar solution with 30.0 mL of a 5.57 M sugar solution will result in a sugar solution with a concentration of 4.542 M.
To find the final concentration of the sugar solution, you need to use the principle of mass conservation. This principle states that the total amount of solute (sugar) before mixing should be equal to the total amount of solute after mixing.
To calculate the final concentration of the sugar solution, you can use the formula:
C₁V₁ + C₂V₂ = C₃V₃
Where:
C₁ = concentration of the first solution (3.00 M)
V₁ = volume of the first solution (20.0 mL)
C₂ = concentration of the second solution (5.57 M)
V₂ = volume of the second solution (30.0 mL)
C₃ = final concentration of the sugar solution (unknown)
V₃ = total volume of the mixed solution (20.0 mL + 30.0 mL = 50.0 mL)
Now, let's substitute the known values into the formula and solve for C₃:
(3.00 M)(20.0 mL) + (5.57 M)(30.0 mL) = C₃(50.0 mL)
(60.0 mL*M) + (167.1 mL*M) = 50.0 mL * C₃
(227.1 mL*M) = 50.0 mL * C₃
C₃ = (227.1 mL*M) / (50.0 mL)
C₃ ≈ 4.542 M
Therefore, when you mix 20.0 mL of a 3.00 M sugar solution with 30.0 mL of a 5.57 M sugar solution, you will end up with a sugar solution of approximately 4.542 M.
Thank you so much for your help! I understood the problem very well (=
1. moles soln 1 = M x L
2. moles soln 2 = M x L
M = total moles/total L