If the detergent requires using 0.61 kg detergent per load of laundry, determine what percentage (by mass) of the detergent should be sodium carbonate in order to completely precipitate all of the calcium and magnesium ions in an average load of laundry water.

Sodium carbonate is often added to laundry detergents to soften hard water and make the detergent more effective. Suppose that a particular detergent mixture is designed to soften hard water that is 3.8×10−3M in Ca2+ and 1.1×10−3M in Mg2+ and that the average capacity of a washing machine is 24.5 gallons of water. 1gallon=3.785L

Answer:

7.90%

Explanation:

The equation for the reaction can be written as:

[tex]Na_2CO_3+Ca^{2+} ---------> CaCO_3(s) +2Na^+[/tex]

[tex]Na_2CO_3+Mg^{2+} ---------> MgCO_3(s) +2Na^+[/tex]

Molar mass of [tex]Na_2CO_3[/tex] = 106 g/mol

1.00 gallon of water = 3.785 L

∴ 24.5 gallons of water = 24.5 × 3.785

= 92.7325 L

mass precipitate = [tex][(3.8*10^{-3})+(1.1*10^{-3})]\frac{mol}{L} *92.7325*\frac{106g}{mol}[/tex]

mass precipitate = 48.162605

mass precipitate = 48.2 g

mass % = [tex]\frac{mass ofprecipitate}{mass of detergent} *100%[/tex]%

mass % = [tex]\frac{48.2g}{0.61kg}*\frac{1kg}{1000g}*100[/tex]%

mass % = 7.901639344

mass % = 7.90 %

andromache andromache · Answer 2 · 2022-03-02T05:51:16+01:00

The percentage (by mass) of the detergent should be 7.90%.

Calculation of the percentage:

Since 3.8×10−3M in Ca2+ and 1.1×10−3M in Mg2+ and that the average capacity of a washing machine is 24.5 gallons of water. 1gallon=3.785L

The molar mass of Na_2CO_3 is 106g/mol

Since 1.00 gallon of water = 3.785 L

so, for 24.5 gallons of water, it is

= 24.5 × 3.785

= 92.7325 L

Now mass precipitate is

= ((3.8*10^-3) * (1.1*10^-3) * 92.7325 * 106g/mol

= 48.162605

= 48.2g

Now the mass percentage is

= mass of precipitate / mass of detergent

= 48.3g / 0.61 * 1kg / 1000g

= 7.90%

This is an incomplete question. Please find the full question below.

Sodium carbonate is often added to laundry detergents to soften hard water and make the detergent more effective. Suppose that a particular detergent mixture is designed to soften hard water that is 3.8×10−3M in Ca2+ and 1.1×10−3M in Mg2+ and that the average capacity of a washing machine is 24.5 gallons of water. 1gallon=3.785L

If the detergent requires using 0.61 kg detergent per load of laundry, determine what percentage (by mass) of the detergent should be sodium carbonate in order to completely precipitate all of the calcium and magnesium ions in an average load of laundry water.

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