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siniylev [52]
3 years ago
5

A 425-ml sample of hydrogen is collected above water at 35°c and 763 torr. find the volume of the hydrogen sample when the tempe

rature falls to 23°c, assuming the barometric pressure does not change. (vapor pressures of water : at 35°c, 42.2 torr ; at 23°c, 21.1 torr)
Chemistry
2 answers:
PilotLPTM [1.2K]3 years ago
5 0
From the gas laws, Charles law states that the volume of a fixed mas of a gas is directly proportional to absolute temperature at constant pressure.
and Boyle's law states that the volume of a fixed mass of a gas is inversely proportional to pressure at constant temperature, therefore combining the two we have, PV/T, for two gases we have,
P1V1/T1=P2V2/T2
V1 = 425 ml, T1= 35 +273 =308 K, P1= 805.2 torr
V2 = ?  and T2 = 23 +273 = 296K, P2 = 784.1torr
  V2 = P1V1T2/P2T1
       = (805.2×425×296)/784×308
       = 419.486 ml
       = 419.5 ml
 
bezimeni [28]3 years ago
5 0

Volume of hydrogen sample at 23^\circ\text{C} is \boxed{419.4\text{ mL}}.

Further Explanation:

Ideal gas equation:

A hypothetical gas comprising of many randomly moving particles having perfectly elastic collisions between them is called ideal gas. The expression for ideal gas equation is mentioned below.

\text{PV}=\text{nRT}                                                      ...... (1)

Here,

P is the pressure of gas.

V is the volume of gas.

T is the absolute temperature of gas.

n is the number of moles of gas.

R is the universal gas constant.

At temperature \text{T}_{1} , volume \text{V}_{1}  and pressure \text{P}_{1} , ideal gas equation for hydrogen gas modifies as follows:

\text{P}_{1}\text{V}_{1}=\text{nRT}_{1}                                                  ...... (2)

At temperature \text{T}_{2} , volume \text{V}_{2}  and pressure \text{P}_{2} , ideal gas equation for hydrogen gas modifies as follows:

\text{P}_{2}\text{V}_{2}=\text{nRT}_{2}                                                  ...... (3)

Dividing equation (3) by equation (2),

\dfrac{\text{P}_{2}\text{V}_{2}}{\text{P}_{1}\text{V}_{1}}=\dfrac{\text{T}_{2}}{\text{T}_{1}}                                                      ...... (4)

Rearrange equation (4) to calculate  .

\text{V}_{2}=\dfrac{{\text{P}_{1}\text{V}_{1}\text{T}_{2}}}{\text{P}_{2}\text{T}_{1}}                                                  …… (5)

The value of \text{P}_{1}  can be calculated as follows:

 \begin{aligned}\text{P}_{1}=&763\text{ torr}+42.2\text{ torr}\\=&805.2\text{ torr}\end{aligned}

The value of \text{P}_{2}  can be calculated as follows:

 \begin{aligned}\text{P}_{2}=&763\text{ torr}+21.1\text{ torr}\\=&784.1\text{ torr}\end{aligned}

The value of  \text{T}_1 can be calculated as follows

\begin{aligned}\text{T}_1=&\left(35+273.15\right)\text{ K}\\=&\ 308.15\text{ K}\end{aligned}

The value of  \text{T}_2 can be calculated as follows

\begin{aligned}\text{T}_2=&\left(23+273.15\right)\text{ K}\\=&\ 296.15\text{ K}\end{aligned}

Substitute 805.2 torr for \text{P}_{1}  , 425 mL for \text{V}_{1} , 784.1 torr for \text{P}_{2} , 308.15 K for \text{T}_{1}  and 296.15 K for \text{T}_{2}  in equation (5).

\begin{aligned}\text{V}_{2}&=\dfrac{\left({805.2\text{ torr}\right)\left(425\text{ mL}\right)\left(296.15\text{ K}\right)}}{\left(784.1\text{ torr}\right)\left(308.15\text{ K}\right)}\\&=419.4\text{ mL}\end{aligned}

Therefore volume of hydrogen sample at 23^\circ\text{ C}  comes out to be 419.4 mL.

Learn more:

1. Which statement is true for Boyle’s law? brainly.com/question/1158880

2. Calculation of volume of gas: brainly.com/question/3636135

Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Ideal gas equation

Keywords: ideal gas equation, R, T, n, P, V, T1, T2, P1, P2, V1, V2, 419.4 mL, pressure, volume, universal gas constant.

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Answer:

The volume of hydrogen gas produced will be approximately 50.7 liters under STP.

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\rm {\bf 1\;Mg}\;(s) + {\bf 2\;HCl}\;(aq) \to ?\;H_2 \;(g)+ {1\;\underset{\wedge}{Mg}\underset{\wedge}{Cl_2}}\;(aq).

The number of \rm H atoms shall also conserve. Hence the equation:

\rm {1\;Mg}\;(s) + {2\;\underset{\wedge}{H}Cl}\;(aq) \to {\bf 1\;H_2 \;(g)}+ {1\;MgCl_2}\;(aq).

How many moles of HCl are available?

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\displaystyle n({\rm HCl}) = \frac{m(\text{HCl})}{M(\text{HCl})} = \rm \frac{165.0\;g}{36.458\;g\cdot mol^{-1}} = 4.52576\;mol.

How many moles of Hydrogen gas will be produced?

Refer to the balanced chemical equation, the coefficient in front of \rm HCl is 2 while the coefficient in front of \rm H_2 is 1. In other words, it will take two moles of \rm HCl to produce one mole of \rm H_2. \rm 4.52576\;mol of \rm HCl will produce only one half as much \rm H_2.

Alternatively, consider the ratio between the coefficient in front of \rm H_2 and \rm HCl is:

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\displaystyle n(\text{H}_2) = n(\text{HCl})\cdot \frac{n(\text{H}_2)}{n(\text{HCl})} = \frac{1}{2}\;n(\text{HCl}) = \rm \frac{1}{2}\times 4.52576\;mol = 2.26288\;mol.

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V(\text{H}_2) = \rm 2.26288\;mol\times 22.7\;L\cdot mol^{-1} = 51.37\; L.

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