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Added general equation for weighted mass average
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Fred
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You have to use mass weighted averaging to calculate the final concentrations of elements. The equation for your situation would be:

$\sf\bar{q}\ =\ \dfrac{m_1.q_1\ +\ m_2.q_2}{m_1\ +\ m_2}\ =\ \dfrac{\rho_1.v_1.q_1\ +\ \rho_2.v_2.q_2}{\rho_1.v_1\ +\ \rho_2.v_2}$

where:

  • $\small\sf m$ is the mass flow rate
  • $\small\sf v$ is the volume flow rate
  • $\small\rho$ is the density of water
  • $\small\sf q$ is the quantity/concentration of the element

Every second, $\small\sf{7000\ L}$ of water flows from River 1 into River 3. Similarly, $\small\sf{11\ m^3}$ of water flows from River 2 into River 3. The combined inflow into River 3 is $\small\sf{18\ m^3}$ every second.

Assuming the density of water in both inflowing rivers is the same, volume of water can be used instead of mass; if not then the density of water for each river needs to be used.

Assuming the water density of both rivers is the same, convert all to units SI units and the average concentration of Mg in River 3 is,

$\sf{\dfrac{7(0.5) + 11(0.34)}{(7 + 11)}}$ = $\sf{0.402\ g/L\ Mg}$

Assuming this is a homework question, I'll let you do the calculation for Ca.

You have to use mass weighted averaging to calculate the final concentrations of elements.

Every second, $\small\sf{7000\ L}$ of water flows from River 1 into River 3. Similarly, $\small\sf{11\ m^3}$ of water flows from River 2 into River 3. The combined inflow into River 3 is $\small\sf{18\ m^3}$ every second.

Assuming the density of water in both inflowing rivers is the same, volume of water can be used instead of mass; if not then the density of water for each river needs to be used.

Assuming the water density of both rivers is the same, convert all to units SI units and the average concentration of Mg in River 3 is,

$\sf{\dfrac{7(0.5) + 11(0.34)}{(7 + 11)}}$ = $\sf{0.402\ g/L\ Mg}$

Assuming this is a homework question, I'll let you do the calculation for Ca.

You have to use mass weighted averaging to calculate the final concentrations of elements. The equation for your situation would be:

$\sf\bar{q}\ =\ \dfrac{m_1.q_1\ +\ m_2.q_2}{m_1\ +\ m_2}\ =\ \dfrac{\rho_1.v_1.q_1\ +\ \rho_2.v_2.q_2}{\rho_1.v_1\ +\ \rho_2.v_2}$

where:

  • $\small\sf m$ is the mass flow rate
  • $\small\sf v$ is the volume flow rate
  • $\small\rho$ is the density of water
  • $\small\sf q$ is the quantity/concentration of the element

Every second, $\small\sf{7000\ L}$ of water flows from River 1 into River 3. Similarly, $\small\sf{11\ m^3}$ of water flows from River 2 into River 3. The combined inflow into River 3 is $\small\sf{18\ m^3}$ every second.

Assuming the density of water in both inflowing rivers is the same, volume of water can be used instead of mass; if not then the density of water for each river needs to be used.

Assuming the water density of both rivers is the same, convert all to units SI units and the average concentration of Mg in River 3 is,

$\sf{\dfrac{7(0.5) + 11(0.34)}{(7 + 11)}}$ = $\sf{0.402\ g/L\ Mg}$

I'll let you do the calculation for Ca.

Decreased font size of MathJax formatted quantities in the body of the text
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Fred
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You have to use mass weighted averaging to calculate the final concentrations of elements.

Every second, $\sf{7000\ L}$$\small\sf{7000\ L}$ of water flows from River 1 into River 3. Similarly, $\sf{11\ m^3}$$\small\sf{11\ m^3}$ of water flows from River 2 into River 3. The combined inflow into River 3 is $\sf{18\ m^3}$$\small\sf{18\ m^3}$ every second.

Assuming the density of water in both inflowing rivers is the same, volume of water can be used instead of mass; if not then the density of water for each river needs to be used.

Assuming the water density of both rivers is the same, convert all to units SI units and the average concentration of Mg in River 3 is,

$\sf{\dfrac{7(0.5) + 11(0.34)}{(7 + 11)}}$ = $\sf{0.402\ g/L\ Mg}$

Assuming this is a homework question, I'll let you do the calculation for Ca.

You have to use mass weighted averaging to calculate the final concentrations of elements.

Every second, $\sf{7000\ L}$ of water flows from River 1 into River 3. Similarly, $\sf{11\ m^3}$ of water flows from River 2 into River 3. The combined inflow into River 3 is $\sf{18\ m^3}$ every second.

Assuming the density of water in both inflowing rivers is the same, volume of water can be used instead of mass; if not then the density of water for each river needs to be used.

Assuming the water density of both rivers is the same, convert all to units SI units and the average concentration of Mg in River 3 is,

$\sf{\dfrac{7(0.5) + 11(0.34)}{(7 + 11)}}$ = $\sf{0.402\ g/L\ Mg}$

Assuming this is a homework question, I'll let you do the calculation for Ca.

You have to use mass weighted averaging to calculate the final concentrations of elements.

Every second, $\small\sf{7000\ L}$ of water flows from River 1 into River 3. Similarly, $\small\sf{11\ m^3}$ of water flows from River 2 into River 3. The combined inflow into River 3 is $\small\sf{18\ m^3}$ every second.

Assuming the density of water in both inflowing rivers is the same, volume of water can be used instead of mass; if not then the density of water for each river needs to be used.

Assuming the water density of both rivers is the same, convert all to units SI units and the average concentration of Mg in River 3 is,

$\sf{\dfrac{7(0.5) + 11(0.34)}{(7 + 11)}}$ = $\sf{0.402\ g/L\ Mg}$

Assuming this is a homework question, I'll let you do the calculation for Ca.

Changed MathJax formatting of calculation
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Fred
  • 25.1k
  • 5
  • 52
  • 96

You have to use mass weighted averaging to calculate the final concentrations of elements.

Every second, $\sf{7000\ L}$ of water flows from River 1 into River 3. Similarly, $\sf{11\ m^3}$ of water flows from River 2 into River 3. The combined inflow into River 3 is $\sf{18\ m^3}$ every second.

Assuming the density of water in both inflowing rivers is the same, volume of water can be used instead of mass; if not then the density of water for each river needs to be used.

Assuming the water density of both rivers is the same, convert all to units SI units and the average concentration of Mg in River 3 is,

$\frac{7(0.5) + 11(0.34)}{(7 + 11)}$$\sf{\dfrac{7(0.5) + 11(0.34)}{(7 + 11)}}$ = 0.402 g/L Mg$\sf{0.402\ g/L\ Mg}$

Assuming this is a homework question, I'll let you do the calculation for Ca.

You have to use mass weighted averaging to calculate the final concentrations of elements.

Every second, $\sf{7000\ L}$ of water flows from River 1 into River 3. Similarly, $\sf{11\ m^3}$ of water flows from River 2 into River 3. The combined inflow into River 3 is $\sf{18\ m^3}$ every second.

Assuming the density of water in both inflowing rivers is the same, volume of water can be used instead of mass; if not then the density of water for each river needs to be used.

Assuming the water density of both rivers is the same, convert all to units SI units and the average concentration of Mg in River 3 is,

$\frac{7(0.5) + 11(0.34)}{(7 + 11)}$ = 0.402 g/L Mg

Assuming this is a homework question, I'll let you do the calculation for Ca.

You have to use mass weighted averaging to calculate the final concentrations of elements.

Every second, $\sf{7000\ L}$ of water flows from River 1 into River 3. Similarly, $\sf{11\ m^3}$ of water flows from River 2 into River 3. The combined inflow into River 3 is $\sf{18\ m^3}$ every second.

Assuming the density of water in both inflowing rivers is the same, volume of water can be used instead of mass; if not then the density of water for each river needs to be used.

Assuming the water density of both rivers is the same, convert all to units SI units and the average concentration of Mg in River 3 is,

$\sf{\dfrac{7(0.5) + 11(0.34)}{(7 + 11)}}$ = $\sf{0.402\ g/L\ Mg}$

Assuming this is a homework question, I'll let you do the calculation for Ca.

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Fred
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