1) A penny has mass of 2.49 g of a volume of o.349 ml. it is heated and it's new volume is found to be 30% greater than the original volume. what is the new density.

2) an ice cream cone has a height of 1.87 x 10⁶ nm and a radius of 2.43 x 10⁶ um. the cone can contain up to 5.23 x 10¹⁴ glucose molecules/pl. one scoop of mint chocolate chip ice cream contains 86 g of glucose. how many scoops of mint chocolate chip ice cream can fit in the cone? (this is very important)

 

1) density: g/mL

(0.349 mL)(1.3)=0.4537 mL

(2.49 g)/(0.4537mL)=5.49 g/mL

2) V=1/3 pi*r²*h (volume of a cone)

1x10⁹ nm = 1 m

(1.87x10⁶ nm)(1 m/1x10⁹ nm)=0.00187 m

1x10⁶ um= 1 m

(2.43x10⁶ um)(1 m/1x10⁶ um)=2.43 m

V=1/3*pi*(2.43 m)²(0.00187)

V=0.01156 m³

1 m³=1000 L

1 L=1x10¹² pL

(0.01156 m³)(1000 L/m³)=11.56 L

(11.56 L)(1x10¹² pL/L)=1.156x10¹³ pL

(1.156x10¹³ pL)(5.23 x 10¹⁴ glucose molecules/pL)=6.05x10²⁷ glucose molecules

molar mass glucose: 180.156 g/mol

(86 g/scoop)/(180.156 g/mol)=0.477 mol/scoop

(0.477 mol/scoop)(6.022x10²³ molecules/mol)=2.87x10²³ glucose molecules/scoop

(6.05x10²⁷ glucose molecules)/(2.87x10²³ glucose molecules/scoop)= 21,066 scoops