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Given that \$\\text{percentage concentration (w/v)}=\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100},\$ which of the following is a valid equation for the volume of the solvent (mL)?

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$\\text{volume of solvent (ml)}=\\dfrac{\\text{mass of solute (g)}}{\\text{percentage concentration (w/v)}}\\times \\text{100}$

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$\\text{volume of solvent (ml)}=\\dfrac{\\text{percentage concentration (w/v)}}{\\text{mass of solute (g)}}\\times \\text{100}$

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$\\text{volume of solvent (ml)}=\\dfrac{\\text{percentage concentration (w/v)}}{\\text{mass of solute (g)}}\\div \\text{100}$

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$\\text{volume of solvent (ml)}=\\dfrac{\\text{mass of solute (g)}}{\\text{percentage concentration (w/v)}}\\div \\text{100}$

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$\\text{volume of solvent (ml)}=\\dfrac{\\text{percentage concentration (w/v)}}{\\text{mass of solute (g)}}$

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$\\text{volume of solvent (ml)}=\\dfrac{\\text{percentage concentration (w/v)}}{\\text{mass of solute (g)}}$

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$\\text{volume of solvent (ml)}=\\dfrac{\\text{mass of solute (g)}}{\\text{percentage concentration (w/v)}}$

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Given that \$\\text{percentage concentration (w/v)}=\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100},\$

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to find an equation for volume of the solvent (mL), we need to get 'volume of solvent (mL)' on to the left side of the equation and then get 'percentage concentration (w/v)' on the right hand side of the equation (so that 'volume of solvent (mL)' is by itself). To do this we multiply both sides by 'volume of solvent (mL)' and divide both sides by 'percentage concentration (w/v)'

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 $\\text{percentage concentration (w/v)}$ $=$ $\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100}$ $\\text{percentage concentration (w/v)}\\times \\text{volume of solvent (mL)}$ $=$ $\\dfrac{\\text{mass of solute (g)}}{\\text{volume of solvent (mL)}}\\times \\text{100}\\times \\text{volume of solvent (mL)}$ $\\text{percentage concentration (w/v)}\\times \\text{volume of solvent (mL)}$ $=$ $\\text{mass of solute (g)}\\times \\text{100}$ $\\dfrac{\\text{percentage concentration (w/v)}\\times \\text{volume of solvent (mL)}}{\\text{percentage concentration (w/v)}}$ $=$ $\\dfrac{\\text{mass of solute (g)}}{\\text{percentage concentration (w/v)}}\\times \\text{100}$ $\\text{volume of solvent (mL)}$ $=$ $\\dfrac{\\text{mass of solute (g)}}{\\text{percentage concentration (w/v)}}\\times \\text{100}$
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