A gas occupies 200ml at a temperature of 26 degrees Celsius and 76mmHg pressure. Find the volume at -3degree Celsius with the pressure remaining constant.

Answer:

184.62 ml

Explanation:

Let [tex]p_1, v_1,[/tex] and [tex]T_1[/tex] be the initial and [tex]p_2, v_2,[/tex] and [tex]T_2[/tex] be the final pressure, volume, and temperature of the gas respectively.

Given that the pressure remains constant, so

[tex]p_1=p_2[/tex] ...(i)

[tex]v_1[/tex] = 200 ml

[tex]T_1= 26 ^{\circ}C = 273+26 =299[/tex] K

[tex]T_2= 3 ^{\circ}C = 273+3 =276[/tex] K

From the ideal gas equation, pv=mRT

Where p is the pressure, v is the volume, T is the temperature in Kelvin, m is the mass of air in kg, R is the specific gas constant.

For the initial condition,

[tex]p_1v_1=mRT_1 \\\\mR= \frac{p_1v_1}{T_1}\cdots(ii)[/tex]

For the final condition,

[tex]p_2v_2=mRT_2 \\\\mR= \frac{p_2v_2}{T_2}\cdots(iii)[/tex]

Equating equation (i), and (ii)

[tex]\frac{p_1v_1}{T_1}=\frac{p_2v_2}{T_2}[/tex]

[tex]\frac{v_1}{T_1}=\frac{v_2}{T_2}[/tex]  [from equation (i)]

[tex]v_2=\frac{T_2}{T_1} \times v_1[/tex]

Putting all the given values, we have

[tex]v_2=\frac{276}{299} \times 200 = 184.62 \; ml[/tex]

Hence, the volume of the gas at 3 degrees Celsius is 184.62 ml.

D
Magnesium carbonate decomposes on heating to form magnesium oxide and carbon dioxide as
shown.
MgCO3 → MgO + CO2
How much magnesium carbonate is needed to make 5.0g of magnesium oxide?
А
3.5g
B 4.09
C 6.5g
D 10.59