   Chapter 20, Problem 97CP

Chapter
Section
Textbook Problem

# Suppose 10.00 g of an alkaline earth metal reacts with 10.0 L water to produce 6.10 L hydrogen gas at 1.00 atm and 25°C. Identify the metal and determine the pH of the solution.

Interpretation Introduction

Interpretation: It is given that, alkaline earth metal reacts with water to produce hydrogen. The mass of unknown alkaline earth metal, volume of water and hydrogen is given. The unknown alkaline earth metal is to be identified. The pH value of this solution is to be calculated.

Concept introduction: The expression to calculate the number of moles by using the ideal gas law is,

PV=nRTn=PVRT

To determine: The unknown alkaline earth metal that when reacts with water produces hydrogen gas; the pH value of this solution.

Explanation

The number of moles of hydrogen gas is 0.249mol_.

Given

Mass of alkaline earth metal is 10.0g.

Volume of water is 10.0L.

Volume of hydrogen gas is 6.10L.

Pressure is 1atm.

Temperature is 25°C.

The conversion of degree Celsius (°C) into Kelvin (K) is done as,

T(K)=T(°C)+273

Hence,

The conversion of 25°C into Kelvin is,

T(K)=T(°C)+273T(K)=(25+273)K=298K

Formula

The number of moles of hydrogen gas is calculated using the formula,

PV=nRTn=PVRT

Where,

• P is the total pressure.
• V is the volume.
• n is the total moles.
• R is the universal gas constant (0.08206Latm/Kmol).
• T is the absolute temperature.

Substitute the values of P,V,R and T in the above equation.

n=PVRT=(1atm)(6.10L)(298K)((0.08206Latm/Kmol))=0.249mol_

The unknown earth metal is calcium (Ca).

Given

Mass of alkaline earth metal is 10.0g.

Volume of water is 10.0L.

It is assumed that the unknown metal is X. The reaction of unknown metal with water is,

X(s)+2H2O(l)H2(g)+X(OH)2(aq)

Since, 0.249mol of hydrogen is formed when metal reacts with water. The number of moles of metal reacted is,

0.249molofH2×1molX1molH2=0.249molofX

Formula

Molar mass of metal is calculated using the formula,

Molarmassofmetal=Givenmass of metalNumberofmolesof metal

Substitute the values of the given mass and number of moles of X in the above equation.

MolarmassofX=Givenmass of XNumberofmolesof X=10

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