Explanation:

\(\mathrm{\mathrm{CaSO}_{4}}\) produces hardness and its solubility in water decreases with rise in temperature.

Explanation:

Explanation:

Clark's process is a commercial method of water softening.
A calculated amount of slaked lime is added to temporary hard water, bicarbonates are converted into insoluble calcium and magnesium carbonates which are filtered off.
\[\rm{\begin{gathered}\mathrm{Ca}(\mathrm{OH})_{2}+2 \mathrm{CO}_{2}=\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2} \\\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}+
\mathrm{Ca}(\mathrm{OH})_{2} \rightarrow 2 \mathrm{CaCO}_{3} \downarrow+2 \mathrm{H}_{2} \mathrm{O}\end{gathered}}\]

Explanation:

Total hardness
\[\frac{\begin{gathered}
{\text{Molarity}}\;\left( {{\text{C}}{{\text{a}}^{{\text{2 + }}}}\;{\mkern 1mu} {\text{and}}\;{\text{M}}{{\text{g}}^{{\text{2 + }}}}} \right) \times \hfill \\
{\text{Molar}}{\mkern 1mu} \;{\text{mass}}{\mkern 1mu} \; {\text{of CaC}}{{\text{O}}_{\text{3}}} \times {\text{10}^6} \hfill \\
\end{gathered} }{{{{10}^3}}}\]
No. of moles of \({\mathrm{\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}=\dfrac{0.81}{162}}}\)
\(=0.005 \mathrm{~mol}\)
\({\mathrm{\therefore}}\) Molarity of \({\mathrm{\mathrm{Ca}^{2+}}}\) ions \({\mathrm{=\dfrac{0.005}{0.1}=0.05 \mathrm{M}}}\)
No. of moles of \({\mathrm{\mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2}=\dfrac{0.73}{146}}}\)
\(=0.005 \mathrm{~mol}\)
\({\mathrm{\therefore}}\) Molarity of \({\mathrm{\mathrm{Mg}^{2+}}}\) ions \({\mathrm{=\dfrac{0.005}{0.1}=0.05 \mathrm{M}}}\)
Hardness in terms of \({\mathrm{\mathrm{CaCO}_{3}}}\)
\({\mathrm{=\dfrac{(0.05+0.05) \times 100}{10^{3}} \times 10^{6}}}\)
\({\mathrm{=10,000 \mathrm{ppm}=1 \times 10^{4} \mathrm{ppm}}}\)
\({\mathrm{\therefore \quad}}\) Value of \({\mathrm{x=4}}\)

Explanation:

Conceptual Questions

Explanation:

\(\mathrm{\mathrm{CaSO}_{4}}\) produces hardness and its solubility in water decreases with rise in temperature.

Explanation:

Explanation:

Clark's process is a commercial method of water softening.
A calculated amount of slaked lime is added to temporary hard water, bicarbonates are converted into insoluble calcium and magnesium carbonates which are filtered off.
\[\rm{\begin{gathered}\mathrm{Ca}(\mathrm{OH})_{2}+2 \mathrm{CO}_{2}=\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2} \\\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}+
\mathrm{Ca}(\mathrm{OH})_{2} \rightarrow 2 \mathrm{CaCO}_{3} \downarrow+2 \mathrm{H}_{2} \mathrm{O}\end{gathered}}\]

Explanation:

Total hardness
\[\frac{\begin{gathered}
{\text{Molarity}}\;\left( {{\text{C}}{{\text{a}}^{{\text{2 + }}}}\;{\mkern 1mu} {\text{and}}\;{\text{M}}{{\text{g}}^{{\text{2 + }}}}} \right) \times \hfill \\
{\text{Molar}}{\mkern 1mu} \;{\text{mass}}{\mkern 1mu} \; {\text{of CaC}}{{\text{O}}_{\text{3}}} \times {\text{10}^6} \hfill \\
\end{gathered} }{{{{10}^3}}}\]
No. of moles of \({\mathrm{\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}=\dfrac{0.81}{162}}}\)
\(=0.005 \mathrm{~mol}\)
\({\mathrm{\therefore}}\) Molarity of \({\mathrm{\mathrm{Ca}^{2+}}}\) ions \({\mathrm{=\dfrac{0.005}{0.1}=0.05 \mathrm{M}}}\)
No. of moles of \({\mathrm{\mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2}=\dfrac{0.73}{146}}}\)
\(=0.005 \mathrm{~mol}\)
\({\mathrm{\therefore}}\) Molarity of \({\mathrm{\mathrm{Mg}^{2+}}}\) ions \({\mathrm{=\dfrac{0.005}{0.1}=0.05 \mathrm{M}}}\)
Hardness in terms of \({\mathrm{\mathrm{CaCO}_{3}}}\)
\({\mathrm{=\dfrac{(0.05+0.05) \times 100}{10^{3}} \times 10^{6}}}\)
\({\mathrm{=10,000 \mathrm{ppm}=1 \times 10^{4} \mathrm{ppm}}}\)
\({\mathrm{\therefore \quad}}\) Value of \({\mathrm{x=4}}\)

Explanation:

Conceptual Questions

Explanation:

\(\mathrm{\mathrm{CaSO}_{4}}\) produces hardness and its solubility in water decreases with rise in temperature.

Explanation:

Explanation:

Clark's process is a commercial method of water softening.
A calculated amount of slaked lime is added to temporary hard water, bicarbonates are converted into insoluble calcium and magnesium carbonates which are filtered off.
\[\rm{\begin{gathered}\mathrm{Ca}(\mathrm{OH})_{2}+2 \mathrm{CO}_{2}=\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2} \\\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}+
\mathrm{Ca}(\mathrm{OH})_{2} \rightarrow 2 \mathrm{CaCO}_{3} \downarrow+2 \mathrm{H}_{2} \mathrm{O}\end{gathered}}\]

Explanation:

Total hardness
\[\frac{\begin{gathered}
{\text{Molarity}}\;\left( {{\text{C}}{{\text{a}}^{{\text{2 + }}}}\;{\mkern 1mu} {\text{and}}\;{\text{M}}{{\text{g}}^{{\text{2 + }}}}} \right) \times \hfill \\
{\text{Molar}}{\mkern 1mu} \;{\text{mass}}{\mkern 1mu} \; {\text{of CaC}}{{\text{O}}_{\text{3}}} \times {\text{10}^6} \hfill \\
\end{gathered} }{{{{10}^3}}}\]
No. of moles of \({\mathrm{\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}=\dfrac{0.81}{162}}}\)
\(=0.005 \mathrm{~mol}\)
\({\mathrm{\therefore}}\) Molarity of \({\mathrm{\mathrm{Ca}^{2+}}}\) ions \({\mathrm{=\dfrac{0.005}{0.1}=0.05 \mathrm{M}}}\)
No. of moles of \({\mathrm{\mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2}=\dfrac{0.73}{146}}}\)
\(=0.005 \mathrm{~mol}\)
\({\mathrm{\therefore}}\) Molarity of \({\mathrm{\mathrm{Mg}^{2+}}}\) ions \({\mathrm{=\dfrac{0.005}{0.1}=0.05 \mathrm{M}}}\)
Hardness in terms of \({\mathrm{\mathrm{CaCO}_{3}}}\)
\({\mathrm{=\dfrac{(0.05+0.05) \times 100}{10^{3}} \times 10^{6}}}\)
\({\mathrm{=10,000 \mathrm{ppm}=1 \times 10^{4} \mathrm{ppm}}}\)
\({\mathrm{\therefore \quad}}\) Value of \({\mathrm{x=4}}\)

Explanation:

Conceptual Questions

Explanation:

\(\mathrm{\mathrm{CaSO}_{4}}\) produces hardness and its solubility in water decreases with rise in temperature.

Explanation:

Explanation:

Clark's process is a commercial method of water softening.
A calculated amount of slaked lime is added to temporary hard water, bicarbonates are converted into insoluble calcium and magnesium carbonates which are filtered off.
\[\rm{\begin{gathered}\mathrm{Ca}(\mathrm{OH})_{2}+2 \mathrm{CO}_{2}=\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2} \\\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}+
\mathrm{Ca}(\mathrm{OH})_{2} \rightarrow 2 \mathrm{CaCO}_{3} \downarrow+2 \mathrm{H}_{2} \mathrm{O}\end{gathered}}\]

Explanation:

Total hardness
\[\frac{\begin{gathered}
{\text{Molarity}}\;\left( {{\text{C}}{{\text{a}}^{{\text{2 + }}}}\;{\mkern 1mu} {\text{and}}\;{\text{M}}{{\text{g}}^{{\text{2 + }}}}} \right) \times \hfill \\
{\text{Molar}}{\mkern 1mu} \;{\text{mass}}{\mkern 1mu} \; {\text{of CaC}}{{\text{O}}_{\text{3}}} \times {\text{10}^6} \hfill \\
\end{gathered} }{{{{10}^3}}}\]
No. of moles of \({\mathrm{\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}=\dfrac{0.81}{162}}}\)
\(=0.005 \mathrm{~mol}\)
\({\mathrm{\therefore}}\) Molarity of \({\mathrm{\mathrm{Ca}^{2+}}}\) ions \({\mathrm{=\dfrac{0.005}{0.1}=0.05 \mathrm{M}}}\)
No. of moles of \({\mathrm{\mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2}=\dfrac{0.73}{146}}}\)
\(=0.005 \mathrm{~mol}\)
\({\mathrm{\therefore}}\) Molarity of \({\mathrm{\mathrm{Mg}^{2+}}}\) ions \({\mathrm{=\dfrac{0.005}{0.1}=0.05 \mathrm{M}}}\)
Hardness in terms of \({\mathrm{\mathrm{CaCO}_{3}}}\)
\({\mathrm{=\dfrac{(0.05+0.05) \times 100}{10^{3}} \times 10^{6}}}\)
\({\mathrm{=10,000 \mathrm{ppm}=1 \times 10^{4} \mathrm{ppm}}}\)
\({\mathrm{\therefore \quad}}\) Value of \({\mathrm{x=4}}\)

Explanation:

Conceptual Questions

Explanation:

\(\mathrm{\mathrm{CaSO}_{4}}\) produces hardness and its solubility in water decreases with rise in temperature.

Explanation:

Explanation:

Clark's process is a commercial method of water softening.
A calculated amount of slaked lime is added to temporary hard water, bicarbonates are converted into insoluble calcium and magnesium carbonates which are filtered off.
\[\rm{\begin{gathered}\mathrm{Ca}(\mathrm{OH})_{2}+2 \mathrm{CO}_{2}=\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2} \\\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}+
\mathrm{Ca}(\mathrm{OH})_{2} \rightarrow 2 \mathrm{CaCO}_{3} \downarrow+2 \mathrm{H}_{2} \mathrm{O}\end{gathered}}\]

Explanation:

Total hardness
\[\frac{\begin{gathered}
{\text{Molarity}}\;\left( {{\text{C}}{{\text{a}}^{{\text{2 + }}}}\;{\mkern 1mu} {\text{and}}\;{\text{M}}{{\text{g}}^{{\text{2 + }}}}} \right) \times \hfill \\
{\text{Molar}}{\mkern 1mu} \;{\text{mass}}{\mkern 1mu} \; {\text{of CaC}}{{\text{O}}_{\text{3}}} \times {\text{10}^6} \hfill \\
\end{gathered} }{{{{10}^3}}}\]
No. of moles of \({\mathrm{\mathrm{Ca}\left(\mathrm{HCO}_{3}\right)_{2}=\dfrac{0.81}{162}}}\)
\(=0.005 \mathrm{~mol}\)
\({\mathrm{\therefore}}\) Molarity of \({\mathrm{\mathrm{Ca}^{2+}}}\) ions \({\mathrm{=\dfrac{0.005}{0.1}=0.05 \mathrm{M}}}\)
No. of moles of \({\mathrm{\mathrm{Mg}\left(\mathrm{HCO}_{3}\right)_{2}=\dfrac{0.73}{146}}}\)
\(=0.005 \mathrm{~mol}\)
\({\mathrm{\therefore}}\) Molarity of \({\mathrm{\mathrm{Mg}^{2+}}}\) ions \({\mathrm{=\dfrac{0.005}{0.1}=0.05 \mathrm{M}}}\)
Hardness in terms of \({\mathrm{\mathrm{CaCO}_{3}}}\)
\({\mathrm{=\dfrac{(0.05+0.05) \times 100}{10^{3}} \times 10^{6}}}\)
\({\mathrm{=10,000 \mathrm{ppm}=1 \times 10^{4} \mathrm{ppm}}}\)
\({\mathrm{\therefore \quad}}\) Value of \({\mathrm{x=4}}\)

Explanation:

Conceptual Questions