What mass of 75% pure CaCO3 will be required to neutralize 50 ml of 0.5M HCL solution according to the following reaction? \[ {CaCO}_3 + 2{HCl} \to {CaCl}_2 + {CO}_2 + {H}_2{O} \]
- Moles of HCl = \( 0.5 \times 0.050 = 0.025 \) moles
- From the reaction, 1 mole of CaCO3 reacts with 2 moles of HCl.
- Moles of CaCO3 required = \( \frac{0.025}{2} = 0.0125 \) moles
- Molar mass of CaCO3 = 100 g/mol, so mass of CaCO3 required = \( 0.0125 \times 100 = 1.25 \) g
- For 75\% pure CaCO3, mass required = \( \frac{1.25}{0.75} = 1.67 \) g
Conclusion: The mass of 75\% pure CaCO3 required is 3.35 g, as given by option (B).
Consider the following half cell reaction $ \text{Cr}_2\text{O}_7^{2-} (\text{aq}) + 6\text{e}^- + 14\text{H}^+ (\text{aq}) \longrightarrow 2\text{Cr}^{3+} (\text{aq}) + 7\text{H}_2\text{O}(1) $
The reaction was conducted with the ratio of $\frac{[\text{Cr}^{3+}]^2}{[\text{Cr}_2\text{O}_7^{2-}]} = 10^{-6}$
The pH value at which the EMF of the half cell will become zero is ____ (nearest integer value)
[Given : standard half cell reduction potential $\text{E}^\circ_{\text{Cr}_2\text{O}_7^{2-}, \text{H}^+/\text{Cr}^{3+}} = 1.33\text{V}, \quad \frac{2.303\text{RT}}{\text{F}} = 0.059\text{V}$
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.