How many moles of ${\text{CaCO}}_{\text{3}}$ required to form $3.01\times {10}^{23}$ molecules of ${\text{CO}}_{\text{2}}$ gas     

${\text{CaCO}}_3\to {\text{CaO+CO}}_2$

$1{\text{ mole of CaCO}}_3{\text{ ----- 1 mole of CO}}_2$

$1{\text{ mole of CaCO}}_3{\text{ ----- 6.023×10}}^{23}{\text{ moles of CO}}_2$

$?{\text{X------ 3.01×10}}^{23}{\text{ molecules of CO}}_2$

$6.023\times {10}^{23}\times \text{X}=1\times 3.01\times {10}^{23}$

$\text{X}=\frac{\cancel{3.01}\times \cancel{{10}^{23}}}{\cancel{6.023}\times \cancel{{10}^{23}}}=\frac{1}{2}{\text{=0.5 moles of CaCO}}_3$