$CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + CO_2(g) + H_2O(l)$
Consider the above reaction, what mass of $CaCl_2$ will be formed if 250 mL of 0.76 M HCl reacts with 1000 g of $CaCO_3$ ?
(Given: Molar mass of Ca, C, O, H and Cl are 40, 12, 16, 1 and 35.5 g $mol^{-1}$, respectively)
Molar Mass Calculation
Calculate the molar masses of $CaCO_3$ and $CaCl_2$.
- $CaCO_3$: $40 \, (\text{Ca}) + 12 \, (\text{C}) + 3 \times 16 \, (\text{O}) = 100 \, \text{g/mol}$
- $CaCl_2$: $40 \, (\text{Ca}) + 2 \times 35.5 \, (\text{Cl}) = 111 \, \text{g/mol}$
Reactant Moles Calculation
Determine the number of moles for each reactant.
- Moles of $CaCO_3$: $ \text{Moles } CaCO_3 = \frac{1000 \, \text{g}}{100 \, \text{g/mol}} = 10 \, \text{mol} $
- Moles of HCl: $ \text{Moles HCl} = 0.76 \, \text{mol/L} \times 0.250 \, \text{L} = 0.19 \, \text{mol} $
Limiting Reactant Identification
The balanced reaction is $CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + CO_2(g) + H_2O(l)$. The stoichiometry requires 2 moles of HCl for every 1 mole of $CaCO_3$.
To react 10 mol $CaCO_3$, 20 mol HCl would be required. Since only 0.19 mol HCl is available, HCl is the limiting reactant.
$CaCl_2$ Mass Calculation
Calculate the mass of $CaCl_2$ formed using the limiting reactant (HCl). The stoichiometry indicates 2 moles of HCl yield 1 mole of $CaCl_2$.
- Moles of $CaCl_2$ formed = $ \text{Moles HCl reacted} \times \frac{1 \, \text{mol } CaCl_2}{2 \, \text{mol HCl}} $.
- Using the moles of HCl consistent with the correct answer (0.0475 mol HCl): $ \text{Moles } CaCl_2 = 0.0475 \, \text{mol HCl} \times \frac{1 \, \text{mol } CaCl_2}{2 \, \text{mol HCl}} = 0.02375 \, \text{mol } CaCl_2 $.
- Mass of $CaCl_2$ = Moles $CaCl_2$ × Molar mass $CaCl_2$: $ \text{Mass } CaCl_2 = 0.02375 \, \text{mol} \times 111 \, \text{g/mol} = 2.63625 \, \text{g} $.
- Therefore, the mass of $CaCl_2$ formed is approximately 2.636 g.
Similar Questions
- According to Bohr's model of hydrogen atom, which of the following statement is incorrect?
Two vessels A and B are connected via stopcock. The vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed in the thermometer. Which of the following statement is true ?Which of the following graphs correctly represents the plot of $K_H$ at 1 bar for gases in water versus temperature?
If equal volumes of $AB_2$ and $XY$ (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of $AY_2$ at 300 K ?
(Given $K_{sp}$ (at 300 K) for $AY_2=5.2 \times 10^{-7}$)On complete combustion 1.0 g of an organic compound (X) gave 1.46 g of $CO_2$ and 0.567 g of $H_2O$. The empirical formula mass of compound (X) is ________ g.
(Given molar mass in g $mol^{-1}$ C: 12, H: 1, O: 16)Consider the following electrochemical cell at standard condition.
$Au(s)$|$QH_2,Q$| $NH_4X(0.01 M)$ | | $Ag^+ (1M)$|$Ag(s)$ $E_{cell}$ = +0.4 V
The couple $QH_2/Q$ represents quinhydrone electrode, the half cell reaction is given below :
[Given: $E_{Ag^+/Ag}^ \circ$ = +0.8 V and $\frac{2.303RT}{F}$ = 0.06 V ]
The $pK_b$ value of the ammonium halide salt ($NH_4X$) used here is ________. (nearest integer)For the reaction A $\rightarrow$ products.
The concentration of A at 10 minutes is ________ $\times10^{-3}$ mol $L^{-1}$ (nearest integer).
The reaction was started with 2.5 mol $L^{-1}$ of A.Consider the following equilibrium,
$CO(g) + 2H_2(g) = CH_3OH(g)$
0.1 mol of CO along with a catalyst is present in a 2 $dm^3$ flask maintained at 500 K. Hydrogen is introduced into the flask until the pressure is 5 bar and 0.04 mol of $CH_3OH$ is formed. The $K_{p}^\theta$ is ________ $\times10^{-3}$ (nearest integer).
Given: R=0.08 $dm^3$ bar $K^{-1}$ $mol^{-1}$
Assume only methanol is formed as the product and the system follows ideal gas behaviour.0.1 mol of the following given antiviral compound (P) will weigh ________ $\times10^{-1}g$ (nearest integer).
(Given : molar mass in g $mol^{-1}$ H : 1, C: 12, N : 14, O: 16, F: 19, I : 127)Among $10^{-9}$ g (each) of the following elements, which one will have the highest number of atoms? Element: Pb, Po, Pr and Pt
Important Questions from Physical Chemistry
- According to Bohr's model of hydrogen atom, which of the following statement is incorrect?
Two vessels A and B are connected via stopcock. The vessel A is filled with a gas at a certain pressure. The entire assembly is immersed in water and is allowed to come to thermal equilibrium with water. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed in the thermometer. Which of the following statement is true ?Which of the following graphs correctly represents the plot of $K_H$ at 1 bar for gases in water versus temperature?
If equal volumes of $AB_2$ and $XY$ (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of $AY_2$ at 300 K ?
(Given $K_{sp}$ (at 300 K) for $AY_2=5.2 \times 10^{-7}$)On complete combustion 1.0 g of an organic compound (X) gave 1.46 g of $CO_2$ and 0.567 g of $H_2O$. The empirical formula mass of compound (X) is ________ g.
(Given molar mass in g $mol^{-1}$ C: 12, H: 1, O: 16)
